# Multiple Choice Probability Calculator

Multiple plot types are available, such as scatter, box-and-whisker, WY-line, histogram, and probability plots. We have already answered 100 questions, so there are only 75 questions left to answer. • The company estimates that the probability of a major accident is 0. Chapter 4: Multiple Choice Questions. (c) the variance of the values. The confidence interval for a proportion is based on the assumption of a large sample size. Sample Math Questions: Multiple-Choice. 22) Ten percent of the population is left - handed. How bad can that be? Frankly, years ago at high school, this was my typical mode of operation. Multiple choice exam in algebra, fractional coefficients, how to do algebra for idiots, practice hall mathmatics, college math made easy. 285) What is the probability that. Sample Space (S)? Set of all possible elementary outcomes of a trial. Practice. Probability Spinners (Basic) FREE Use the pictures of the spinners to determine the probability of outcomes for events. Sorry for incomplete answers. com Tel: 800-234-2933;. (b) Determine the probability of drawing a ction book rst and then a hardcover book second, when drawing without replacement. A probability distribution is a table or an equation that links each outcome of a statistical experiment with its probability of occurrence. We proceed with the above example. Since we are guessing our way through the multiple choice questions, our probability of success in each question will be $\frac{1}{4}$ Since the pass mark is $\frac{123}{175}$, we need at least $\frac{23}{75}$ in the final 75 questions. What's the probability that the next person you speak to has pets? a) 1/4 b) 1 c) 1/25 d) 4/25 2. Suppose further that the student has to guess randomly on each question. Mean and Variance of Random Variables Mean The mean of a discrete random variable X is a weighted average of the possible values that the random variable can take. A teacher tempted to give your students multiple choice tests ? Got to pass a multiple choice test such as an IQ test or something similar? Do you know what you are getting yourself in to ? Science in Action : Probability and statistics in Multiple Choice, or how to beat the odds and pass a multiple choice test effortlessly (or : a fair way of. Algebra -> Probability-and-statistics-> SOLUTION: The probability of answering a multiple choice questions correctly by guessing is 0. Convert the 22) binomial probability P(x < 12) to a normal probability by using the correction for continuity. Calculate the probability that a randomly chosen member of this group visits a X3 be a random sample from a discrete. Multiple choice questions d. Examination 110 – Probability and Statistics Examination Sample Examination Questions The Probability and Statistics Examination consists of 45 multiple-choice test questions. Let's say there are 5 multiple choice questions, with the answers A, B or C. Basic Probability Concepts. The science of counting is captured by a branch of mathematics called combinatorics. a) Before doing any calculations, the mean for this b) Calculate the mean. Long answer questions e. In other words,the empty set ϕ is an impossible event and the sample space S is a sure event. If each question has four choices and you guess on each question, what is the probability of getting exactly 7 questions correct? n = 10 k = 7 n – k = 3. You may not use a calculator during this session. And since It showed up on my GRE , I can't recollect the answer choices correctly. A variety of different problems can be solved using the Texas Instruments graphing calculator. 22) Ten percent of the population is left - handed. The probability of getting heads at least twice is 11/16. Page last modified 07/07/2017 17:21:51. MULTIPLE CHOICE. Probability Calculator You can use this Probability Calculator to determine the probability of single and multiple events. CSE 103: Probability and statistics Fall 2010 Topic 2 — Multiple events, conditioning, and independence, II 2. The use of a multiple-choice format for hour exams at many institutions leads to a deluge of statistical data, which are often neglected or completely ignored. Set up the binomial probability formula to find the probability of getting e Log On. In our example multiple-choice test, whether you guess randomly or choose 'C' every time, you would expect, on average, to get 30*0. The present re-analysis shows that MCP data are compatible with behavioral economic analysis of drug choices. , a binomial probability), given the number of successes, the number of trials, and the probability of a successful outcome occurring. For example: 1 roll: 5/6 (83. Tossing a coin gives a 50% chance of getting heads or tails. a) Before doing any calculations, the mean for this b) Calculate the mean. p n Expected value. Here is a simple probability model for multiple-choice tests. CALCULATING THE PROBABILITIES OF WINNING LOTTO 6/49 VERSION 3 : MARCH 1, 2003 The probability of event tells us how likely it is that the event will occur and is always a value between 0 and 1 (e. More about the z-test for one population proportion so you can better interpret the results obtained by this solver: A z-test for one proportion is a hypothesis test that attempts to make a claim about the population proportion (p) for a certain population attribute (proportion of males, proportion of people underage). (d) the sampling distribution of the statistic. The mean is n*p and the variance is sqrt[n*p*(1-p)], where n is the number of trials and p is the probability of the desired outcome. Counting and Probability Probability is the mathematical study of chance and random processes. Advanced (for programmers) The binompdf( and binomcdf( commands are the only ones apart from seq( that can return a list of a given length, and they do it much more quickly. AP Stats Multiple-Choice Questions Chap 18-19 Name _____ Pd _____ MULTIPLE CHOICE. Problem Description: A multiple choice test has four possible answers to each of 16 questions. Try the multiple choice questions below to test your knowledge of this Chapter. The probability of getting heads at least twice is 11/16. The measure of location which is the most likely to be influenced by extreme values in the data set is the a. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing. Example: Problem #14, you'll need to multiply 1,200,000 by 365, but the answer has to be greater than 365,000,000, which only leaves one choice for the correct answer. Six math questions also have grid-in answers, and one math question is an extended thinking question, with a. In the example you gave, I find it much easier to start by calculating the probability of NOT rolling a 5 across multilple throws, because these probabilities can be just multiplied together. Using the TI84 calculator follow the steps below: From the MATH button, choose PRB and select option 5: We wish to generate 20 different answers. ) C Functions & Algebra 1 2 11 Multiple-choice (1 pt. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing. Items 8 through 50 are in the calculator section of the test. Compute the probability/odds of selecting the first five numbers and add to it the probability/odds of selecting the Bonus Ball number. What's the probability that the next person you speak to has pets? a) 1/4 b) 1 c) 1/25 d) 4/25 2. What is distribution of values taken by a statistic in all possible samples of the same size from the same population called? (a) the probability that the statistic is obtained. Andrea has 8 blue socks and 4 red socks. Choose the response that best answers the question. Multiple-choice tests. Positively skewed C. 98 in the case that the tested individual uses the drug) and 90% accurate in the case of a non-user of the drig (e. com's short, multiple choice quizzes. Hi, the question is a multiple choice question. Now, part (b) should be simple, by Bayes formula. 25 probability of 1 girl, etc. What's the probability that the next person you speak to has pets? a) 1/4 b) 1 c) 1/25 d) 4/25 2. com Tel: 800-234-2933;. a student randomly guesses at five multiple-choice questions, each question has five possible choices (suppose the choice for each question is independent): a) Find the probability that the student gets exactly three correct. a What is the expected value of the number Y of questions that will be correctly answered?. Posted from my mobile device. Unformatted text preview: Chapter 07 Continuous Probability Distributions Multiple Choice Questions 16. Probability calculator is a online tool that computes probability of selected event based on probability of other events. Probability is the ideal of relative frequency - Multiple Choice Questions In Class IX, you have studied about experimental (or empirical) probabilities of events which were based on the results of actual experiments. Probability lesson plans and worksheets from This one-page learning exercise contains five multiple-choice problems. 25% of a population have pets. Probability/Counting Multiple Choice Post-Test Multiple Choice Identify the choice that best completes the statement or answers the question. asked by Pamela Straw on November 1, 2012; Statistics. If we plot the likelihood of rolling a 6 on a dice in the probability line, it would look something like this:. Using the TI84 calculator follow the steps below: From the MATH button, choose PRB and select option 5: We wish to generate 20 different answers. 13) Expected relative frequency probability represents a calculated probability based on large numbers of trials. With the probability calculator you can investigate the relationships of likelihood between two separate events. Assess student understanding of arithmetic, algebra, and geometry concepts with these math worksheets for K-12 students. What is the sum of the probabilities in a uniform probability distribution? a. You randomly guess each question. For example, if the chance of A happening is 50%, and the same for B, what are the chances of both happening, only one happening , at least one happening, or neither happening, and so on. Pascal decided to allow her students to determine what kind of test the class would write. performance on one quiz has no bearing on the other quiz). MULTIPLE CHOICE. 25 probability of 1 girl, etc. A student guesses blindly on a 20-question multiple choice test. You are taking a multiple choice quiz that consist in 3 questions, each question has 3 possible answers only one is correct. Probability is a measure of the likelihood that an event will occur. Which one of the following ways should they use to select a representative sample. And even just having one really obvious bad choice in each problem is enough to change the odds materially - I calculate better than 8% of at least 13 matches if there are only 2 good distractors. More about the z-test for one population proportion so you can better interpret the results obtained by this solver: A z-test for one proportion is a hypothesis test that attempts to make a claim about the population proportion (p) for a certain population attribute (proportion of males, proportion of people underage). Probability of the union of A and B: P( A ∪ B ) Probability of intersection of A and B: P( A ∩ B. Probability distributions multiple choice questions and answers (MCQs), probability distributions quiz answers, MBA business statistics test prep 16 to learn online statistics courses for online classes. Find the experimental probability of getting tails. Each time she got a tails. STATISTICS 8 CHAPTERS 1 TO 6, SAMPLE MULTIPLE CHOICE QUESTIONS Correct answers are in bold italics. This applet should work in IE but may be slow. choice, but each element can have a different chance of being selected. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes. Skip navigation Probability explained Khan Academy 3,772,428 views. If you blindfolded yourself and randomly guessed at three multiple choice questions with 5 choices, what is the probability you get all 3 correct? Calculators and. (c) Calculate the probability of the scenario in part (b), except this time complete the calculations under the scenario where the rst book is placed back on the bookcase before randomly drawing the second book. Find the probability of getting a queen and a red card. a probability of 1/4 means one chance out of four, or 25%. In the example you gave, I find it much easier to start by calculating the probability of NOT rolling a 5 across multilple throws, because these probabilities can be just multiplied together. My assumption is that you would choose A after reading the question and the answers (and considering them). We reviewed using AP multiple choice test-prep flashcards and old AP exam FRQs. The PDF is the density of probability rather than the probability mass. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975 ( Selvin 1975a ), ( Selvin 1975b ). Each question has four possible responses. Predictions: (a) Before doing any formal analysis, make some predictions:. c) the researcher has a certain quota of respondents to fill for various social groups. b) at least to answer correctly. Assess student understanding of arithmetic, algebra, and geometry concepts with these math worksheets for K-12 students. For this calculator, the order of the items chosen in the subset does not matter. The concept is very similar to mass density in physics: its unit is probability per unit length. I need a multiple choice Graphing calculator, printable retangle grid samples, real life examples of ellipses, program calculator "slope formula", free algebra worksheets, finding scale factors. The TI-Nspire™ CX CAS graphing calculator provides algebraic capability to symbolically solve equations, factor and expand variable expressions, complete the square, find antiderivatives, computer limits and exact solutions in irrational forms, making it a robust hands-learning tool that satisfies. The possible results of the action are classified as "success" or "failure". In what follows, S is the sample space of the experiment in question and E is the event of interest. Suppose it is known that 0. Please enter the necessary parameter values, and then click 'Calculate'. We draw 10 bulbs without replacement. Tutorial on finding the probability of an event. Probability of strictly guessing on a multiple choice test? Someone posted this question on another message board (but I know THIS is the place to get an answer). The use of a graphing calculator in AP Statistics is considered an integral part of the course. 5, the probability that they will be able to eliminate one choice is 0. Summary: To find the probability of event A or B, we must first determine whether the events are mutually exclusive or non-mutually exclusive. Larger numbers indicate greater likelihood. Tips from ACT including test taking, multiple choice questions, calculator and writing tips. Find the probability of getting a queen and a red card. Suppose further that the student has to guess randomly on each question. Time --- 1 hour and 30 minutes. There, you will find scoring. In our example multiple-choice test, whether you guess randomly or choose 'C' every time, you would expect, on average, to get 30*0. You program a computer to pick an option randomly. Since Richard has not attended class recently, he doesn't know any of the answers. A Stats 10 test has 4 multiple choice questions with four choices with one correct answer each. Determine whether the Normal model may be used to describe the distribution of the sample proportions. This free calculator can compute the number of possible permutations and combinations when selecting r elements from a set of n elements. Suppose that the weights of trucks traveling on the interstate highway system are normally distributed. Let X˜be˜the discrete random variable that Cassandra answers the question correctly. Posc/Uapp 816 Class 14 Multiple Regression With Categorical Data Page 3 1. Online homework and grading tools for instructors and students that reinforce student learning through practice and instant feedback. Improve your math knowledge with free questions in "Find the probability" and thousands of other math skills. asked by Pamela Straw on November 1, 2012; Statistics. Mixed Probability Word Problems Worksheet 1 - What is the chance of randomly choosing a dress, lotto choices, and numbers. Each multiple choice correct response is worth 3 points. Interquartile range 7. 444%) probability of NOT rolling a 5. Nothing is certain in this quiz. The possible results of the action are classified as "success" or "failure". A multiple choice test has 5 questions each with 5 possible answers. -----Figure 3-4----- In sampling without replacement (WOR) the selection process is the same as at step one ) that is each addict in the population has the same probability of being selected (Figure 3-4, bottom). This unit on probability covers how to use simulations to calculate experimental probabilities and a variety of other methods (the addition rule, the multiplication rule, conditional probability) for calculating probability. Tossing a coin gives a 50% chance of getting heads or tails. Read More Asked in Probability. Greatest Common Factor (gcf. Mathematics multiple-choice questions will be used mainly to assess standard algorithms. When you take a multiple-choice exam, the chances of guessing the correct answer are usually 1 out of 4, or 25 %. expectation rates. Choose the one alternative that best completes the statement or answers the question. cfw 1(None)c 4 1(CALC) Result Screen Result : p. -Multiple choices: "Travel to work in rush hour,"and "travel to work out of rush hour,"as well as the choice of bus or car. what is the probability that a student would get more than 18 answers correct simply by guessing?. A student has studied enough so that the probability they will know the answer to a question is 0. Writing Multiple Choice and True/False Exam Questions: A Good Practice Guide 1. In response to this, we’ll discuss Savage’s (1954) approach to choice under uncertainty, which rather than assuming the existence of objective probabilities attached to uncertain prospects 1. Even so, multiple-choice questions seem to make up the bulk of the questions on most of the exams. A uniform probability model occurs when all the probabilities in a probability model are equally likely to occur. Calculation problems c. (a) If each question has four different choices, find the probability that Erin gets one or more correct answers on a 10-item quiz. Probability/Counting Multiple Choice Post-Test Multiple Choice Identify the choice that best completes the statement or answers the question. In 2020, the AP Statistics exam will take place on Friday, May 15th at 12:00pm. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes. During the next 55-minute SAT Math section, you are allowed to use your calculator. This exam is composed of 25 multiple choice questions each worth 4 points. Probability Word Problems (Cards and Dice) Worksheet 1 - Only the second one requires a tree diagram, the others are two-steps. No tasks yet illustrate this standard. In an example of a deck of 52 cards, where you randomly pull cards from the deck and record what they are, you find that over 1000 random draws, you pull an ACE 76 times. Each time she got a tails. As you can see, there are six combinations of the three colors. d) every unit of the population has an equal chance of being selected. 1 Basic De nitions Trials? Probability is concerned with the outcome of tri-als. Using my calculator I get: n = 24. Discrete probability distributions MCQs, probability distributions quiz questions and answers for admission and merit scholarships test. Probability Calculation. The probability of getting heads at least twice is 11/16. Express the indicated degree of likelihood as a probability value. If the number of trials be ‘n’ and the probability of occurrence be ‘p’ then the standard deviation with respect to np, is given by: a. This is a practice test for the multiple-choice section of the Advanced Placement Statistics Exam. 1 are estimates. Calculation problems c. Printable Math Worksheets, Tests, and Activities. Assuming that there are 5 choices for each multiple-choice question, then we take the probability that the student who guesses will be correct is 1 / 5 = 0. This unit on probability covers how to use simulations to calculate experimental probabilities and a variety of other methods (the addition rule, the multiplication rule, conditional probability) for calculating probability. DIRECTIONS This session contains eight multiple-choice questions, two short-answer questions, and one open-. The student gets 5 correct 2. Calculate the probability p that the ﬁrst extracted was white, when the second is white. University of Delaware. I have been known to request copies of answer keys from teachers to table the distribution of answers. Therefore, the probability of an event lies between 0 ≤ P(A) ≤ 1. I am a college student who is slightly obsessed with working out the answers to problems like these. It is mainly concerned with the amount of time until some specific event occurs. The only reason we were able to calculate these probabilities is because we recognized that this was a binomial experiment. How to Calculate Probability With and Without Replacement V2. Nothing is certain in this quiz. You are taking a multiple choice quiz that consist in 3 questions, each question has 3 possible answers only one is correct. Section 2 does not permit the use of a calculator and has a time limit of 55 minutes. Rounding a number is calculating an approximate value using truncation of its digits/decimal places (rounding down floor, rounding up ceil, rounding to multiple) in the limits of the precision asked to the calculator. I only need 12 answers correct to pass the entire class with a B. They may not resemble the questions that your instructor may ask on a test. The actual exam is not multiple choice nor does it contain like questions. Multiple Choice: 1. For your record, also circle your choice on your exam since the scantron will not be returned to you. You may not use a calculator during this session. Now, part (b) should be simple, by Bayes formula. Find the indicated probability. The world's most trusted Texas hold'em poker odds calculator. Larger numbers indicate greater likelihood. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 50 %. You randomly guess each question. you are to circle the correct answer. Multiple plot types are available, such as scatter, box-and-whisker, WY-line, histogram, and probability plots. The probability of getting heads at least twice is 11/16. Read More Asked in Probability. This fact allowed us to use binompdf for exact probabilities and binomcdf for probabilities that included multiple values. I am about to take a 50 question multiple choice test with four possible answers a,b,c,d. Very simple probability question regarding multiple choice questions Say you have a normal multiple choice question you don't know the answer to. The concept is very similar to mass density in physics: its unit is probability per unit length. Calculates the probability mass function and I just wanted to calculate the probably of someone passing a 100 question multiple choice test by guessing every. What is the probability. If two events (both with probability greater than 0) are mutually exclusive, then: A. This calculator will tell you the one-tailed and two-tailed probability values of a t-test, given the t-value and the degrees of freedom. And since It showed up on my GRE , I can't recollect the answer choices correctly. 2) Find the probability of correctly answering the first 2 questions on a multiple choice test if random guesses are made and each question has 3 possible answers. The binomial probability formula is used to find probabilities for Bernoulli trials. In addition, schools should make every effort to. a probability of 1/4 means one chance out of four, or 25%. The score on each section is converted to a 15 point scale so that your total score has a maximum value of 45. These examples include flipping coins, drawing cards from a deck, guessing on a multiple choice test, selecting jellybeans from a bag, and choosing people for a committee, etc. Math Grade 7 Page 17. The question styles found in this section are multiple choice (40 questions) and gridded response (12 questions). Missed some things?. 22) Ten percent of the population is left - handed. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975 ( Selvin 1975a ), ( Selvin 1975b ). When it comes to online to verify or perform such calculations, this online binomial distribution calculator may help users to make the calculation as simple as possible. I need a multiple choice Graphing calculator, printable retangle grid samples, real life examples of ellipses, program calculator "slope formula", free algebra worksheets, finding scale factors. This is a practice test for the multiple-choice section of the Advanced Placement Statistics Exam. The multiple choice questions on the Long-Term Actuarial Mathematics exam are intended to average five minutes each. Navy/Flickr Ideally, multiple-choice exams would be random, without patterns of right or wrong answers. Lessons distinguishing between theoretical probability and experimental probability, How to find and use experimental probability, How to find the theoretical probability of an event, How to use the formula for theoretical probability, examples with step by step solutions, questions and answers. The probability of any member attending a randomly chosen meeting is 0. calculator. We reviewed using AP multiple choice test-prep flashcards and old AP exam FRQs. In 2020, the AP Statistics exam will take place on Friday, May 15th at 12:00pm. I have been known to request copies of answer keys from teachers to table the distribution of answers. Multiple Choice Practice Set 1 This set of questions covers material from Chapter 1. When you get your score, you will be shown the correct answers. a student randomly guesses at five multiple-choice questions, each question has five possible choices (suppose the choice for each question is independent): a) Find the probability that the student gets exactly three correct. Now that we have finished our discussion of derivatives of functions of more than one variable we need to move on to integrals of functions of two or three variables. Take the time to write out the work, with correct notation and treat it like a free response as well! Double the practice!. The science of counting is captured by a branch of mathematics called combinatorics. • What is the expected value of the policy to the insurance company? 14 Insurance Example - 2 Outcomes Probability Cost to Premium company major accident minor accident no accident 0. 23) A question has five multiple-choice answers. The question styles found in this section are multiple choice (40 questions) and gridded response (12 questions). A student guesses blindly on a 20-question multiple choice test. Multiple choice is the same format as for the midterm. Multiple-Choice Section. The chance that you get it correct by random guessing would be $\frac13$. Mathematics multiple-choice questions will be used mainly to assess standard algorithms. Classical Probability cannot be used:. Suppose further that the student has to guess randomly on each question. Mean, mode and median are basic statistical tools used to calculate different types of averages. Sorry for incomplete answers. you decide to guess for each of these questions. Given that arrivals are random over a one hour period and follow the Poisson probability distribution then the (arrival) calculation of P(3) is: probability of an arrival within 3 hours probability of 3 arrivals each hour. So for example if there are 4 red balls and 3 yellow balls in a bag, the probability of choosing a red ball will be 4/7. The shorter the accounting period the more accurate is the profit calculation B. 0625 probability of no girls, a. Item is still being reviewed Multiple Choice ZSCORE STANDERROR/OTHER STANDUNITS/NORMA PROBDISTRIBUTION PROBABILITY DESCRSTAT/P PARAMETRIC STATISTICS T= 5 Application D= 4 Business General ***Calculator Necessary*** ***Statistical Table Necessary***. They also could be independent. Drug testing example for conditional probability Suppose that a drug test for an illegaldrug is such that it is 98% accurate in the case of a user of that drug (e. Both methods make assumptions which weaken their use under actual classroom testing situations. Preview Print Answers. Find the probability of getting a queen and a red card. Mean, mode and median are basic statistical tools used to calculate different types of averages. MULTIPLE CHOICE QUESTIONS (50%) All answers must be written on the answer sheet; write answers to five questions in each row, for example: 1. Anyway, if someone were just to make outright guesses on a 60 question multiple choice test (5 choices per question), what is the probability of getting 40 correct?. The last set of notes for Chapter 4 can be found here. Assess student understanding of arithmetic, algebra, and geometry concepts with these math worksheets for K-12 students. The probability of an event is a number between 0 and 1 that represents the likelihood of that event occurring. Only the responses. The Probability Calculator computes the probability of one event, based on probabilities of other events. Click here for older java version of this applet. Become a Subscriber to access all standards aligned worksheets. 1 Conditional probability, continued 2. You may not use a calculator for session 1, but you may use a calculator for sessions 2 and 3. Example: no 2,a,b,c means that an. 25% of a population have pets. Online homework and grading tools for instructors and students that reinforce student learning through practice and instant feedback. SCORING: 40 Multiple Choice Questions. Multiple Choice: 1. Item is not too easy: if the probability of getting the item correct is too high, the item will not differentiate participants on the construct measured. 1 However, a formal, precise deﬁnition of the probability is elusive. We want the probability of correct, correct, and correct. Only the responses. We have already answered 100 questions, so there are only 75 questions left to answer. Basic Probability 1. In Calculus I we moved on to the subject of integrals once we had finished the discussion of derivatives. A bag contains 4 red, 11 green, and 5 blue balls. This exam is composed of 25 multiple choice questions each worth 4 points. Multiple Choice: 1. References Multiple Choice Learning Objective: 05-02 Identify and apply the appropriate approach to assigning probabilities. Long answer questions e. X is binomial with n = 10, p = 0. 5, the probability that they will be able to eliminate one choice is 0. Navy/Flickr Ideally, multiple-choice exams would be random, without patterns of right or wrong answers. Probability: Guessing on a multiple-choice test. You may use a calculator, and notes on three sides of a standard 8. 6 So we can go back and check. Negatively skewed B. a Construct a probability distribution table for X. The binomial distribution is a _____ probability distribution (a) categorical (b)discrete (c) continuous 2. you decide to guess for each of these questions. To calculate mean, you simple add up all the values of data given and divide by the number data provided. This chapter. Section 2 does not permit the use of a calculator and has a time limit of 55 minutes. The fact-checkers, whose work is more and more important for those who prefer facts over lies, police the line between fact and falsehood on a day-to-day basis, and do a great job. Today, my small contribution is to pass along a very good overview that reflects on one of Trump’s favorite overarching falsehoods. Namely: Trump describes an America in which everything was going down the tubes under  Obama, which is why we needed Trump to make America great again. And he claims that this project has come to fruition, with America setting records for prosperity under his leadership and guidance. “Obama bad; Trump good” is pretty much his analysis in all areas and measurement of U.S. activity, especially economically. Even if this were true, it would reflect poorly on Trump’s character, but it has the added problem of being false, a big lie made up of many small ones. Personally, I don’t assume that all economic measurements directly reflect the leadership of whoever occupies the Oval Office, nor am I smart enough to figure out what causes what in the economy. But the idea that presidents get the credit or the blame for the economy during their tenure is a political fact of life. Trump, in his adorable, immodest mendacity, not only claims credit for everything good that happens in the economy, but tells people, literally and specifically, that they have to vote for him even if they hate him, because without his guidance, their 401(k) accounts “will go down the tubes.” That would be offensive even if it were true, but it is utterly false. The stock market has been on a 10-year run of steady gains that began in 2009, the year Barack Obama was inaugurated. But why would anyone care about that? It’s only an unarguable, stubborn fact. Still, speaking of facts, there are so many measurements and indicators of how the economy is doing, that those not committed to an honest investigation can find evidence for whatever they want to believe. Trump and his most committed followers want to believe that everything was terrible under Barack Obama and great under Trump. That’s baloney. Anyone who believes that believes something false. And a series of charts and graphs published Monday in the Washington Post and explained by Economics Correspondent Heather Long provides the data that tells the tale. The details are complicated. Click through to the link above and you’ll learn much. But the overview is pretty simply this: The U.S. economy had a major meltdown in the last year of the George W. Bush presidency. Again, I’m not smart enough to know how much of this was Bush’s “fault.” But he had been in office for six years when the trouble started. So, if it’s ever reasonable to hold a president accountable for the performance of the economy, the timeline is bad for Bush. GDP growth went negative. Job growth fell sharply and then went negative. Median household income shrank. The Dow Jones Industrial Average dropped by more than 5,000 points! U.S. manufacturing output plunged, as did average home values, as did average hourly wages, as did measures of consumer confidence and most other indicators of economic health. (Backup for that is contained in the Post piece I linked to above.) Barack Obama inherited that mess of falling numbers, which continued during his first year in office, 2009, as he put in place policies designed to turn it around. By 2010, Obama’s second year, pretty much all of the negative numbers had turned positive. By the time Obama was up for reelection in 2012, all of them were headed in the right direction, which is certainly among the reasons voters gave him a second term by a solid (not landslide) margin. Basically, all of those good numbers continued throughout the second Obama term. The U.S. GDP, probably the single best measure of how the economy is doing, grew by 2.9 percent in 2015, which was Obama’s seventh year in office and was the best GDP growth number since before the crash of the late Bush years. GDP growth slowed to 1.6 percent in 2016, which may have been among the indicators that supported Trump’s campaign-year argument that everything was going to hell and only he could fix it. During the first year of Trump, GDP growth grew to 2.4 percent, which is decent but not great and anyway, a reasonable person would acknowledge that — to the degree that economic performance is to the credit or blame of the president — the performance in the first year of a new president is a mixture of the old and new policies. In Trump’s second year, 2018, the GDP grew 2.9 percent, equaling Obama’s best year, and so far in 2019, the growth rate has fallen to 2.1 percent, a mediocre number and a decline for which Trump presumably accepts no responsibility and blames either Nancy Pelosi, Ilhan Omar or, if he can swing it, Barack Obama. I suppose it’s natural for a president to want to take credit for everything good that happens on his (or someday her) watch, but not the blame for anything bad. Trump is more blatant about this than most. If we judge by his bad but remarkably steady approval ratings (today, according to the average maintained by 538.com, it’s 41.9 approval/ 53.7 disapproval) the pretty-good economy is not winning him new supporters, nor is his constant exaggeration of his accomplishments costing him many old ones). I already offered it above, but the full Washington Post workup of these numbers, and commentary/explanation by economics correspondent Heather Long, are here. On a related matter, if you care about what used to be called fiscal conservatism, which is the belief that federal debt and deficit matter, here’s a New York Times analysis, based on Congressional Budget Office data, suggesting that the annual budget deficit (that’s the amount the government borrows every year reflecting that amount by which federal spending exceeds revenues) which fell steadily during the Obama years, from a peak of $1.4 trillion at the beginning of the Obama administration, to$585 billion in 2016 (Obama’s last year in office), will be back up to $960 billion this fiscal year, and back over$1 trillion in 2020. (Here’s the New York Times piece detailing those numbers.) Trump is currently floating various tax cuts for the rich and the poor that will presumably worsen those projections, if passed. As the Times piece reported: