AP Stats Chapter 6 Test PDF

Name: ________________________ Class: ___________________ Date: __________ ID: B AP Stats Chapter 6 Test Multiple Choice Identify the choice that best completes the statement or answers the question. ____ e 1. In the town of Tower Hill, the number of cell...

Name: ________________________ Class: ___________________ Date: __________ ID: B AP Stats Chapter 6 Test Multiple Choice Identify the choice that best completes the statement or answers the question. ____ e 1. In the town of Tower Hill, the number of cell phones in a household is a random variable W with the following distribution: Number of cell phones wi 0 1 2 3 4 5 Probability pi 0.1 0.1 0.25 0.3 0.2 0.05 What is the probability that a randomly selected household has at least two cell phones? a. 0.20 b. 0.25 c. 0.55 px 2 25 t 3 t 2 t 05 d. 0.70 e. 0.80 d ____ 2. Which of the following is a true statement? a. The binomial setting requires that there are only two possible outcomes for each trial, while the geometric setting permits more than two outcomes. b. A geometric random variable takes on integer values from 0 to n. c. If X is a geometric random variable and the probability of success is 0.85, then the probability distribution of X will be skewed to the left, since 0.85 is closer to 1 than to 0. d. An important difference between binomial and geometric random variables is that there is a fixed number of trials in a binomial setting, and the number of trials varies in a geometric setting. e. The distribution of every binomial random variable is skewed to the right. 1 Name: ________________________ ID: B a ____ 3. A college basketball player makes 80% of her free throws. At the end of a game, her team is losing by two points. She is fouled attempting a three-point shot and is awarded three free throws. Assuming free throw attempts are independent, what is the probability that she makes at least two of the free throws? a. 0.896 b. 0.80 c. 0.64 binomial pdf d. 0.512 x 21 X 3 e. 0.384 d gÉ 384 0.512 C ____ 4. Jocelyn has a babysitting business. Based on daily sales figures for the past two years, she has developed the following probability distribution for X = daily profit (in dollars). Daily profit xi 0 10 20 30 Probability pi 0.2 0.4 0.3 0.1 Which of the following is the expected value of X? a. $3.25 b. $10 c. $13 5 13 d. $15 e. $18 b ____ 5. A worn out bottling machine does not properly apply caps to 5% of the bottles it fills. If you randomly select 20 bottles from those produced by this machine, what is the approximate probability that exactly 2 caps have been improperly applied? a. 0.0002 b. 0.19 binomial pdf c. 0.74 d. 0.81 e. 0.92 P x2 0.19 2 Name: ________________________ ID: B b ____ 6. Roll one 8-sided die 10 times. What is the probability of getting exactly 3 sevens in those 10 rolls? a. x b. I p i p c. i d. e. c ____ 7. The mp3 music files on Sharon’s computer have a mean size of 4.0 megabytes and a standard deviation of 1.8 megabytes. She wants to create a mix of 10 of the songs for a friend. Let the random variable T = the total size (in megabytes) for 10 randomly selected songs from Sharon’s computer. Typically, the formula 1.07(file size) – 0.02 provides a good estimate of the length of a song in minutes. If M = 1.07T – 0.02, the mean and standard deviation of M will be approximately a. b. c. d. e. d ____ 8. In order for the random variable X to have a geometric distribution, which one of the following conditions must X satisfy? a. p < 0.5 b. The number of trials is fixed. c. X = the number of successes in n trials. d. The probability of success has to be the same for each trial. e. All outcomes in the sample space are equally likely. 3 Name: ________________________ ID: B a ____ 9. Jen’s commute to work requires that she take the Blue subway line and then transfer to the Red line. The length of the trip on the Blue line has a mean of 18 minutes and a standard deviation of 2 minutes. The length of the trip on the Red line has a mean of 12 minutes and a standard deviation of 1 minute. The waiting time between when she gets off the Blue line and her Red line train arrives has a mean of 10 minutes and a standard deviation of 5 minutes. Assume these times are independent random variables. The mean and standard deviation of her entire commute will be approximately a. Mean = 40 minutes; Standard deviation = 8 minutes. b. Mean = 40 minutes; Standard deviation = 5.48 minutes. c. Mean = 40 minutes; Standard deviation = 2.83 minutes. d. Mean = 30 minutes; Standard deviation = 5.48 minutes. e. Mean = 30 minutes; Standard deviation = 8 minutes. b 10. You are stuck at the Vince Lombardi rest stop on the New Jersey Turnpike with a dead battery. To get on the ____ road again, you need to find someone with jumper cables that connect the batteries of two cars together so you can start your car again. Suppose that 16% of drivers in New Jersey carry jumper cables in their trunk. You begin to ask random people getting out of their cars if they have jumper cables. You’re going to give up and call a tow truck if you don’t find jumper cables by the time you’ve asked 10 people. What’s the probability you end up calling a tow truck? a. 0.8251 b. 0.1749 c. 0.1344 d. 0.0333 e. 0.0280 a 11. The weight of written reports produced in a certain department has a Normal distribution with a mean of 60 ____ grams and a standard deviation of 12 grams. What is the probability that the next report will weigh less than 45 grams? a. 0.1056 b. 0.3944 c. 0.1042 d. 0.0418 e. 0.8944 4 Name: ________________________ ID: B a 12. A poll shows that 60% of the adults in a large town are registered Democrats. A newspaper reporter wants to ____ interview a local democrat regarding a recent decision by the City Council. On average, how many people will the reporter have to stop before he finds his first Democrat? a. 1 b. 1.33 geometric c. 1.67 d. 2 e. 2.33 5 Name: ________________________ ID: B Free Response Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of yourmethods as well as on the accuracy and completeness of your results and explanations. 13. Determine whether the random variable described below satisfies the conditions for a binomial setting, a geometric setting, or neither. Support your conclusion. (a) Suppose that 1 of every 100 people in a large community is infected with HIV. You want to identify an HIV-positive person to include in a study of an experimental new drug. You would like to determine how many individuals you would expect to randomly select in order to find the first person who is HIV-positive. B success HIV t failure HIV condition is I reasonable toassume population is largerthan1000 samplingwithoutreplacement met T until successoccurs S probabilityof success isequal in eachtrial geometric 14. Suppose that the mean height of policemen is 70 inches with a standard deviation of 3 inches. And suppose that the mean height for policewomen is 65 inches with a standard deviation of 2.5 inches. If heights of policemen and policewomen are Normally distributed, find the probability that a randomly selected policewoman is taller than a randomly selected policeman. Interpret this probability. not geometric or binomial because theprobability ofsuccess is notequal foreachtrial 6 Name: ________________________ ID: B 15. An online poll reported that 20% of respondents subscribe to the “five-second rule.” That is, they would eat a piece of food that fell onto the kitchen floor if it was picked up within five seconds. Let’s assume this figure is accurate for the entire U.S. population, and we select 15 people at random from this population. Let F = the number of people in our sample of 15 who subscribe to the “five-second rule.” (a) Determine the probability that exactly 3 of the 15 people subscribe to the “five-second rule.” binomialpdf 15 3,1 0.25 (b) Find the probability that fewer than 4 people out of 15 subscribe to the “five-second rule.” binomialCdf 0.65 1,5 3 (c) Find and interpret the expected value of F. 0.2 15 3 We wouldexpect 3 of the 15people in the sample to subscribe to the 5secondrule (d) Find and interpret the standard deviation of F. 1.55 the number of people in thesample whosubscribe tothe 5 second rule varies on average by1.55 7 Formulas for AP Statistics I. Descriptive Statistics 2 1 xi 1 2 xi x x xi  sx  xi x  n n n 1 n 1 ŷ  a bx y  a bx 1 xi x yi y sy r br n 1 sx sy sx II. Probability and Distributions P ( A  B) P A B P A P B P A B P ( A | B)  P ( B) Probability Distribution Mean Standard Deviation Discrete random variable, X µ X = E ( X ) =  xi ⋅ P ( x i ) (x − µ X ) ⋅ P ( xi ) 2 σX = i If X has a binomial distribution with  X  np  np 1 p X parameters n and p, then: n n x P Xx  px 1 p x where x  0, 1, 2, 3,  , n If X has a geometric distribution with 1 1 p parameter p , then: X   p X p x 1 P Xx  1 p p where x  1, 2, 3,  III. Sampling Distributions and Inferential Statistics statistic − parameter Standardized test statistic: standard error of the statistic Confidence interval: statistic ± ( critical value )( standard error of statistic ) ( observed − expected ) 2 Chi-square statistic: χ =  2 expected AP Statistics Course and Exam Description Appendix V.1 | 254 Return to Table of Contents © 2019 College Board III. Sampling Distributions and Inferential Statistics (continued) Sampling distributions for proportions: Standard Error* of Random Variable Parameters of Sampling Distribution Sample Statistic For one population: p 1 p pˆ 1 pˆ p̂  p̂  p pˆ  s pˆ  n n For two populations: p1 1 p1 p2 1 p2 pˆ1 1 pˆ1 pˆ 2 1 pˆ 2 pˆ1 − pˆ2  pˆ pˆ2  p1 p2 pˆ1 pˆ 2  s pˆ1 pˆ2  1 n1 n2 n1 n2 When p1  p2 is assumed: 1 1 s pˆ1 − pˆ2 = pˆc (1 − pˆc ) + n1 n2 X1 X 2 where pˆ c  n1 n2 Sampling distributions for means: Standard Error* of Random Variable Parameters of Sampling Distribution Sample Statistic For one population: s X    sX  X X n n For two populations: 2 2 s12 s22 X1 X2 X X2  1 2 X1 X 2  1 2 s X1 X2  1 n1 n2 n1 n2 Sampling distributions for simple linear regression: Standard Error* of Random Variable Parameters of Sampling Distribution Sample Statistic For slope: , s b   sb  , b b n sx n 1 x 2 xi x yi yi 2 where x  where s n n 2 2 xi x and sx  n 1 *Standard deviation is a measurement of variability from the theoretical population. Standard error is the estimate of the standard deviation. If the standard deviation of the statistic is assumed to be known, then the standard deviation should be used instead of the standard error. AP Statistics Course and Exam Description Appendix V.1 | 255 Return to Table of Contents © 2019 College Board