AP Statistics - Ms. Cowart's Teacher Page - Home



Chapter 16 and 17 Practice Test Name______________________________

AP Statistics Period_______

Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.

1. Sixty-five percent of all divorce cases cite incompatibility as the underlying reason. If four couples file for a divorce, what is the probability that exactly two will state incompatibility as the reason?

A) .104

B) .207

C) .254

D) .311

E) .423

2. Which of the following are true statements?

I. The histogram of a binomial distribution with p = .5 is always symmetric.

II. The histogram of a binomial distribution with p = .9 is skewed to the right.

III. The histogram of a geometric distribution is always decreasing.

A) I and II

B) I and III

C) II and III

D) I, II, and III

E) None of the above gives the complete set of complete responses.

3. Binomial and geometric probability situations share many conditions. Identify the choice that is not shared.

A) The probability of success on each trial is the same.

B) There are only two outcomes on each trial.

C) The focus of the problem is the number of successes in a given number of trials.

D) The probability of a success equals 1 minus the probability of a failure.

E) The mean depends on the probability of a success.

4. In a population of students, the number of calculators owned is a random variable X with P(X = 0) = 0.2, P(X = 1) = 0.6, and P(X = 2) = 0.2. The mean of this probability distribution is

A) 0

B) 2

C) 1

D) 0.5

E) The answer cannot be computed from the information given.

5. Refer to the previous problem. The variance of this probability distribution is

A) 1

B) 0.63

C) 0.5

D) 0.4

E) The answer cannot be computed from the information given.

6. A recent study of the BHS student body determined that 41% of the students were “cool”. If Mr. Dimsdale has developed a test for “cool-ness”, what is the average number of students we would need to test in order to find one who is “cool”?

A) 2

B) 2.44

C) 3

D) 3.57

E) 1, because the study is clearly in error since all BHS students are “cool”

7. The color distribution in a bag of Reese’s Pieces was found to be 13 brown, 22 orange, and 15 yellow. If a piece is randomly drawn and replaced, what is the probability that it will take less than 8 draws to get an orange piece?

A) .014

B) .008

C) .990

D) .983

E) .500

8. The weight of reports produced in a certain department has a normal distribution with mean 60g and standard deviation 12g. What is the probability that the next report will weigh less than 45g?

A) 0.1042

B) 0.1056

C) 0.3944

D) 0.0418

E) The answer cannot be computed from the information given.

9. Which of the following statements is NOT correct?

A) The number of successes that corresponds to the maximum value of a binomial PDF is within one unit of its mean.

B) A geometric PDF is always decreasing.

C) A binomial PDF with p < .5 will be skewed right.

D) As the number of trials in a geometric situation increases and the number of successes in a binomial situation increases, the value of the CDF approaches 0.

E) A PDF can be transformed into a CDF by using addition.

10. A renowned soccer player scores a goal on 30% of his attempts. The random variable X is defined as the number of goals scored on 50 attempts.

A renowned gambler wins at Blackjack 25% of the time. The random variable Y is defined as the number of games needed to win his first game.

Define the random variable Z as the total number of soccer goals scored and blackjack games played. Determine the mean of the random variable Z.

A) 11

B) 19

C) 10

D) 9.5

E) Cannot be determined with the given information.

Part II – Free Response (Question 11-13) – Show your work and explain your results clearly.

11. Tennessee Jed, a professional dart player, has an 80% chance of hitting the bullseye on a dartboard with any throw.

Suppose that he throws 10 darts, one at a time, at the dartboard.

a) Find the probability that Jed hits the bullseye exactly six times.

b) Find the probability that he hits the bullseye at least six times.

c) Compute the number of expected bullseyes in 10 throws.

d) Compute the standard deviation of the expected number of bullseyes in 10 throws.

Jed is playing darts with his uncle, John, who is not a professional. John has a 35% chance of hitting the bullseye.

e) Find the probability that John’s first bulls eye occurs on the fourth throw.

f) Find the probability that it takes John less than five throws to hit the bullseye.

g) What is the expected number of throws for John to hit the bullseye?

12. Two swimmers have been training for a big race in the 100 meter backstroke. Their times are known to be normally distributed with the following distributions (in seconds). We can also assume that the times of the two swimmers are independent.

Swimmer 1: mean = 77.9, standard deviation = 2.49

Swimmer 2: mean = 76.76, standard deviation = 3.08

a) The swimmers keep track of their progress over the season. What is the mean of the first swimmers time (x) minus the second swimmers time (y)?

[pic]

b) What is the standard deviation of the first swimmers time (x) minus the second swimmers time (y)?

[pic]

c) Using these results, what is the probability the second swimmer will beat the first swimmer on any given race? Remember the lowest time wins.

13. A distribution of grades in an introductory statistics class (where A = 4, B = 3, etc.) is:

X 0 1 2 3 4

p(X) .10 .15 .30 .30 .15

a) A graduate student needs at least a B to get credit for the course. What are her chances of getting at least a B?

b) Find P(1 ≤ X < 3).

c) Find the average (i.e., mean) grade in this class.

d) Find the standard deviation for the class grades.

e) Find the lowest grade [pic] such that [pic]. Your answer should be either a 0, 1, 2, 3, or 4.

f) Circle the correct answer: X is an example of a ( discrete ) ( continuous ) random variable.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download