The practice test follows this cover sheet. It is very similar to the real Chapter Test.

Transcription

1 AP Stats Unit IV (Chapters 14-17) Take-Home Test Info The practice test follows this cover sheet. It is very similar to the real Chapter Test. The real test will consist of 20 multiple-choice questions (Section I) consist of three shorter free-response questions (Section II, Part A) consist of one more involved free-response question (Section II, Part B) be ed to you Tuesday evening, March 9, 2010 be due at class time Tuesday, March 16 / Wednesday, March 17, Similar to the last take-home test, you may work with anyone else in your class or the other class. In fact you SHOULD plan on working with each other! You must accomplish the exact version of the test that will be ed to you! Turning in answers to a different version will be considered academic dishonesty. I will be available in room 141 Monday evening, March 15, from 6:30 8pm for assistance with this Practice Test only. I will NOT be answering questions on the real test. Good luck.

2 AP Stats Chap Practice Test SECTION I Number of Questions 20 Percent of Total Grade 50 Directions: Solve each of the following problems, using the available space (or extra paper) for scratchwork. Decide which is the best of the choices given and place that letter on the ScanTron sheet. No credit will be given for anything written on these pages for this part of the test. Do not spend too much time on any one problem. 1. Which two events are most likely to be independent? A. having a flat tire, and being late for school B. getting an A in math, and getting an A in Physics C. having a driver s license, and having blue eyes D. having a car accident, and having three inches of snow today E. being a senior, and leaving campus for lunch 2. Political analysts estimate the probability that Hillary Clinton will run for president in 2008 is 45% and the probability that New York s Governor George Pataki will run as the Republican candidate is 20%. If their political decisions are independent, then what is the probability that only Hillary runs for president? A. 9% B. 11% C. 25% D. 36% E. 45% 3. In an AP Stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. Forty-six percent of students eat breakfast and also floss their teeth. What is the probability that a student from this class eats breakfast but does not floss his/her teeth? A. 9% B. 11% C. 34% D. 57% E. 91% 4. The city council has six men and three women. If we randomly choose two of them to co-chair a committee, what is the probability these chairpersons are the same gender? A. 4/9 B. 1/2 C. 5/9 D. 5/8 E. 7/8 5. Which of these random variables has a geometric model? A. the number of cards of each suit in a ten-card hand B. the number of people we check until we find someone with green eyes C. the number of cars inspected until we find three with bad mufflers D. the number of Democrats among a group of 20 randomly chosen adults E. the number of aces among the top ten cards in a well-shuffled deck 6. You are dealt a hand of three cards, one at a time. Find the probability that your cards are all diamonds. A B C D E

3 7. An ice cream stand reports that 12% of the cones they sell are Jumbo size. You want to see what a Jumbo cone looks like, so you stand and watch the sales for a while. What is the probability that the first Jumbo cone is the fourth cone you see them sell? A. 8% B. 33% C. 40% D. 60% E. 93% 8. What is the probability there is exactly one Jumbo among the first six cones sold by the ice cream stand in Question 7? A. 6% B. 12% C. 38% D. 54% E. 84% 9. A friend of your plans to toss a fair coin 200 times. You watch the first 20 tosses and are surprised that she got 15 heads. But then you get bored and leave. How many heads do you expect her to have when she has finished all 200 tosses? A. 100 B. 169 C. 110 D. 115 E A pool of possible jurors consists of 11 men and 14 women. A jury of 12 is picked at random from this group. You are interested in determining the probability that the jury contains all women. Can a probability model based on a Bernoulli trial be used to investigate this situation? A. Yes. B. Yes, assuming the possible jurors are unrelated. C. No. There are more that two possible outcomes on each trial. D. No. the chance of a woman changes depending on who has already been picked. E. No. Eleven is more than 10% of A basketball player has made 66% of his foul shots during the season. Assuming the shots are independent, find the probability that in tonight s game he misses for the first time on his sixth attempt. A B C D E Suppose that in a certain population 44% of people have type O blood. A researcher selects people at random from this population. What s the probability they won t find a person with type O blood among the first seven people checked? A B C D E An airline, believing that 6% of passengers fail to show up for flights, overbooks. Suppose a plane will hold 320 passengers and the airline sells 335 seats. What is the probability the airline will not have enough seats and will have to bump someone? A B C D E

4 14. Police estimate that in one city 59% of drivers wear their seat belts. They set up a safety roadblock, stopping cars to check for seat belt use. If they stop 30 cars during the first hour, what is the mean number of drivers expected to be wearing their seat belts? A B C D. 15 E On a multiple choice test with 13 questions, each question has four possible answers, one of which is correct. For students who guess at all the answers, find the standard deviation of the number of correct answers. A. 1.5 B C D E A laboratory worker finds that 1.6% of his blood samples test positive for the HIV virus. If 240 blood samples are selected at random, is it appropriate to use a Normal model to approximate the distribution of the number that test positive for the virus? A. No. A Normal model cannot be used to approximate the distribution because nq < 10. B. Yes. A Normal model with µ = 3.84 and σ = 3.78 can be used to approximate the distribution. C. No. A Normal model cannot be used to approximate the distribution because np <10. D. Yes. A Normal model with µ = and σ = 1.94 can be used to approximate the distribution. E. Yes. A Normal model with µ = 3.84 and σ = 1.94 can be used to approximate the distribution. 17. A tennis player usually makes a successful first serve 73% of the time. She buys a new racket hoping that is will improve her success rate. During the first month of playing with her new racket, she makes 327 successful first serves out of 410. Is this evidence that with the new racket her success rate has improved? In other words, is this an unusual result for her? A. Yes. We would normally expect her to make first serves with a standard deviation of is 0.3 standard deviations above the expected value. That s an unusual result. B. No. We would normally expect her to make first serves with a standard deviation of is 0.3 standard deviations above the expected value. That s not an unusual result. C. Yes. We would normally expect her to make first serves with a standard deviation of is 3.1 standard deviations above the expected value. That s an unusual result. D. No. We would normally expect her to make first serves with a standard deviation of is 1.6 standard deviations above the expected value. That s not an unusual result. E. No. We would normally expect her to make first serves with a standard deviation of is 3.1 standard deviations above the expected value. That s not an unusual result.

5 18. A carnival game offers a $100 cash prize for anyone who can break a balloon by throwing a dart at it. It costs $8 to play and you re willing to spend up to $32 trying to win. You estimate that you have a 10% chance of hitting the balloon on any throw. Find the expected amount you will win. Assume that throws are independent of each other. A. $9.27 B. $6.88 C. $14.88 D. -$11.52 E. -$ Your favorite soccer team, Mill Valley, plays two games against Fairfield. The probability that your team wins the first game is 0.4. If your team wins the first game, the probability that they also win the second game is 0.4. If your team loses the first game, the probability that they win the second game is 0.2. Let the random variable X be the number of games won by your team. Find the standard deviation of X. A B C D E A manufacturing process has a 70% yield, meaning 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable. A B C D. 2.1 E. 0.9 SECTION II Part A 3 Questions (similar to the following) Percent of Section II Grade 75 SECTION II Part B 1 Question (similar to the following) Percent of Section II Grade 25 Directions: Show all of your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanations. Traffic Accidents. 21. Police reports about the traffic accidents they investigated last year indicated that 40% of the accidents involved speeding, 25% involved alcohol, and 10% involved both risk factors. a. What is the probability that an accident involved neither alcohol nor speed? b. Do these two risk factors appear to be independent? Explain using statistical evidence.

6 Bowling. 22. A large corporation sponsors bowling leagues for its employees. The mean score for men was 154 pins with a standard deviation of nine pins, while the women had a mean score of 144 pins and a standard deviation 12 pins. At the end of the season the league holds a tournament that randomly pairs men and women as opponents in the first round. a. On average, how much do you expect the man to win by? b. Estimate the standard deviation of the differences in the competitor s scores. c. What assumption did you make in determining the standard deviation? Smoking. 23. Virginia public health officials claim that 18% of adults currently smoke cigarettes. a. We start by selecting a few adults at random, asking each if he or she is a smoker. Explain why these can be considered Bernoulli trials. b. How many people do you expect to have to ask in order to find a smoker? c. Let X represent the number of smokers among a randomly chosen sample of 30 adults. Find the mean and standard deviation of X. d. What is the probability that there are at least eight smokers among our sample of 30 people? e. What is the probability that the first smoker, in our group of 30, is the fifth person we ask? Seatbelts. 24. Safety officials hope a public information campaign will increase the use of seatbelts above the current 70% level. Their efforts include running radio and TV ads, putting up billboards, having police officers appear on talk shows, and getting newspapers to indicate whether people injured in accidents were belted in. After several months they check the effectiveness of this campaign with a statewide survey of 560 randomly chosen drivers. Four hundred seven of those drivers report that they wear a seatbelt. a. Verify that a Normal model is a good approximation for the binomial model in this situation. b. Does the survey result suggest that the education / advertising campaign was effective? Defend your opinion.