AP Statistics - University of Arizona



AP Statistics Name ______________

Chapter 14 -15 Review

1. If P(A) = .2 and P(B) = .1, what is [pic] if A and B are independent?

A. .02

B. .28

C. .30

D. .32

E. The is insufficient information to answer the question

Questions 2- 6, refer to the following study. One thousand students at a city high school were classified both according to GPA and whether or not they consistently skipped classes.

GPA

| |< 2.0 |2.0 – 3.0 |> 3.0 |TOTAL |

|Many skipped classes |80 |25 |5 |110 |

|Few skipped classes |175 |450 |265 |890 |

|TOTAL |255 |475 |270 |1000 |

2. What is the probability that a student has a GPA between 2.0 and 3.0?

A. .025 B. .227 C. .450 D. .475 E. .506

3. What is the probability that a student has a GPA under 2.0 and has skipped many classes?

A. .080 B. .281 C. .285 D. .314 E. .727

4. What is the probability that a student has a GPA under 2.0 or has skipped many classes?

A. .080 B. .281 C. .285 D. .314 E. .727

5. What is the probability that a student has a GPA under 2.0 given that he has skipped many classes?

A. .080 B. .281 C. .285 D. .314 E. .727

6. Are GPA between 2.0 and 3.0 and Skipped few classes independent?

A. No, because .475 ( .506

B. No, because .475 ( .890

C. No, because .450 ( .475

D. Yes, because of conditional probabilities

E. Yes, because of the product rule

Questions 7 – 10, refer to the following study: Five hundred people used a home test for HIV, and then all underwent more conclusive hospital testing. The accuracy of the home test was evidenced in the following table.

| |HIV |Healthy |TOTAL |

|Positive Test |35 |25 |60 |

|Negative Test |5 |435 |440 |

|TOTAL |40 |460 | |

7. What is the predictive value of the test? That is, what is the probability that a person has HIV and tests positive?

A. .070 B. .130 C. .538 D. .583 E. .875

8. What is the false-positive rate? That is, what is the probability of testing positive given that the person does not have HIV?

A. .054 B. .050 C. .130 D. .417 E. .875

9. What is the sensitivity of the test? That is, what is the probability of testing positive given that the person has HIV?

A. .070 B. .130 C. .538 D. .583 E. .875

10. What is the probability of testing negative given that the person does not have HIV?

A. .125 B. .583 C. .870 D. .950 E. .946

11. A consumer organization estimates that 29% of new cars have a cosmetic defect, such as a scratch or a dent, when they are delivered to car dealers. This same organization believes that 7% have a functional defect—something that does not work properly— and that 2% of new cars have both kinds of problems.

a) If you buy a new car, what’s the probability that it has some kind of defect?

__________.34__________

b) What’s the probability it has a cosmetic defect but no functional defect?

__________.27_________

c) If you notice a dent on a new car, what’s the probability it has a functional defect?

_________.069_________

d) Are the two kinds of defects disjoint events? Explain.

No, because the [pic]=0.02 not zero

e) Do you think the two kinds of defects are independent events? Explain.

Yes they are independent. [pic] .07 = .07

12. A company’s human resources officer reports a breakdown of employees by job type and gender, shown in the table. Gender

| | |Male |Female |

|Job Type |management |7 |6 |

| |supervision |8 |12 |

| |Production |45 |72 |

What’s the probability that a worker selected at random is

a. Female? _______.6________________

b. Female or a production worker? _______.9________________

c. Female, if the person works in production? _______.615______________

d. A production worker, if the person is female? _______.8________________

13. Since the stock market began in 1872, stock prices have risen in about 73% of the years. Assuming that market performance is independent from year to year, what’s the probability that

a) The market will rise for 3 consecutive years? .389

b) The market will fall during at least 1 of the next 5 years? .793

14. The Centers for Disease Control say that about 30% of high-school students smoke tobacco (down from a high of 38% in 1997). Suppose you randomly select high-school students to survey them on their attitudes toward scenes of smoking in the movies. What’s the probability that

a) None of the first 4 students you interview is a smoker? .2401

b) The first smoker is the sixth person you choose? .0504

15. Molly’s college offers two sections of Statistics 101. From what she has heard about the two professors listed, Molly estimates that her chances of passing the course are 0.80 if she gets professor Scedastic and 0.60 if she gets Professor Kurtosis. The registrar uses a lottery to randomly assign the 120 enrolled students based on the number of available seats in each class. There are 70 seats in Professor Scedastic’s class and 50 in Professor Kurtosis’s class.

a) What’s the probability that Molly will pass Statistics? .7167

b) At the end of the semester, we find out that Molly failed. What’s the probability that she got

Professor Kurtosis?

.5882

16. The 2000 Census revealed that 26% of all firms in the United States are owned by women. You call some firms doing business locally, assuming that the national percentage is true in your area.

a) What’s the probability that the first 3 you call are all owned by women? .018

b) What’s the probability that none of your first 4 calls finds a firm that is owned by a woman?

.2999

17. Every 5 years the Conference Board of the Mathematical Sciences surveys college math departments. In 2000 the board reported that 51% of all undergraduates taking Calculus I were in classes that used graphing calculators and 31% were in classes that used computer assignments. Suppose that 16% used both calculators and computers.

a) What percent used neither kind of technology? .34

b) What percent used calculators but not computers? .35

c) What percent had computer assignments given they were calculator users? .314

d) Based on this survey do calculator and computer use appear to be independent events? Explain.

Yes, they are independent .314 = .314

18. A census by the county dog control officer found that 18% of homes kept one dog as a pet, 4% had two dogs, and 1% had three or more. If a salesman visits two homes selected at random, what’s the probability he encounters

a) no dogs? _______.5929___________

b) some dogs? _______.0529___________

c) more than one dog in each home? ________.0025__________

19. In your sock drawer you have 4 blue socks, 5 grey socks, and 3 black ones. Half asleep one morning, you grab 2 socks at random and put them on. Find the probability you end up wearing

a) 2 blue socks. ____.091______________

b) No grey socks. _____.318_____________

c) At least 1 black sock. ____.455______________

d) A green sock. ______0____________

20. In the table what are the [pic]and [pic]?

| |D |E |TOTAL |

|A |15 |12 |27 |

|B |15 |23 |38 |

|C |32 |28 |60 |

|TOTAL |62 |63 |125 |

A. [pic] B. [pic] C. [pic] D. [pic] E. [pic]

21. For the tree diagram pictured, what is [pic]?

B. [pic] B. [pic] C. [pic] D. [pic] E. [pic]

22. The GPA (grade point average) of students who take the AP Statistics exam are approximately normally distributed with a mean of 3.4 with a standard deviation of 0.3. What is the probability that a student selected at random from this group has a GPA lower than 3.0?

A. 0.0918 B. 0.4082 C. 0.9082 D. -.0918 E. 0

23. The 2000 Census identified the ethnic breakdown of the state of California to be approximately as follow: White: 46%, Latino: 32%, Asian: 11%, Black: 7%, and Other: 4%. Assuming that these are mutually exclusive categories (this is not a realistic assumption, especially in California), what is the probability that a random selected person from the state of California is of Asian or Latino decent?

A. 46% B. 32% C. 11% D. 43% E. 3.5%

24. The students in problem #22 above were normally distributed with a mean GPA of 3.4 and standard deviation of 0.3. In order to qualify for the school honor society, a student must have a GPA in the top 5% of all GPAs. Accurate to two decimal places, what is the minimum GPA Norma can have in order to qualify for the honor society?

A. 3.95 B. 3.92 C. 3.75 D. 3.85 E. 3.89

25. Given that[pic].

A. Find [pic] = _______.3____________________________________

B. Find [pic] = _______.6____________________________________

C. Are events A and B independent? Explain your answer.

No they are not independent. [pic] .05 [pic]= .03

26. Harvey, Laura, and Gina take turns throwing spit-wads at a target. Harvey hits the target [pic] of the time. Laura hits it [pic] of the time, and Gina hits the target [pic] of the time. Given that somebody hit the target, what is the probability that it was Laura?

[pic]

27. A normal distribution has mean 700 and standard deviation 50. The probability is 0.6 that a randomly selected term from this distribution is above x. What is x?

X = 687.33

28. Suppose that 80% of the homes in the Woodlands have a desktop computer and 30% have both a desktop computer and a laptop computer. What is the probability that a randomly selected home will have a laptop computer given that they have a desktop computer?

.375

29. Conroe has an annual pumpkin festival at Halloween. A prime attraction to this festival is a “largest pumpkin” contest. Suppose that the weights of these pumpkins are approximately normally distributed with a mean of 125 pounds and a standard deviation of 18 pounds. Farmer Riley brings a pumpkin that is at the 90% percentile of all the pumpkins in the contest. What is the approximate weight of Riley’s pumpkin?

X= 148.07

30. Consider the following two probability distributions for independent discrete random variable X and Y.

X |2 |3 |4 | |Y |3 |4 |5 |6 | |P(X) |0.3 |0.5 |? .2 | |P(X) |? .15 |0.1 |? .55 |0.4 | |

If [pic], what is [pic]?

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