8 in a large population of college students 20 of the

8. In a large population of college students, 20% of the students have experienced feelings of
math anxiety. If you take a random sample of 10 students from this population, the mean
and standard deviation of the number of students in the sample who have experienced math
anxiety is:
(a) P = 1.6; V = 1.414
(b) P = 1.6; V = 1.265
(c) P = 2; V = 1.6
(d) P = 2; V = 1.414
(e) P = 2; V = 1.265

¶º Which of the following is a true statement?
.
© 2011 BFW Publishers The Practice of Statistics, 4/e- Chapter 6 277

278 The Practice of Statistics, 4/e- Chapter 6 © 2011 BFW Publishers
Part 2: Free Response
Show all 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 and completeness of your results and
explanations.
10. A company that rents DVDs from vending machines in grocery stores has developed the
following probability distribution for the random variable X = the number of DVDs a
customer rents per visit to a machine.
(a) Find and interpret the mean (expected value) of X
(b) Find and interpret the standard deviation of X
(c) Suppose the profit the company makes on each customer visit is $0.75 per DVD minus
$0.05 “fixed costs.” That is, if P = profit, then 0.75 0.05. P X µ Use a linear
transformation of your results in (a) and (b) to find the mean and standard deviation for
P .
X 1 2
P(X) 0.5 0.3 0.1
.
.
3 4
0.1

© 2011 BFW Publishers The Practice of Statistics, 4/e- Chapter 6 279
11. ACT scores for the 1,171,460 members of the 2004 high school graduating class who took
the test closely followed the Normal distribution with mean 20.9 and standard deviation 4.8.
Choose two students independently and at random from this group.
(a) What is the expected difference in their scores?
(b) What is the standard deviation of the difference in their scores?
(c) Find the probability that the difference in the two students’ scores is greater than 6.
12. A professional soccer player succeeds in scoring a goal on 84% of his penalty kicks. Assume
that the success of each kick is independent.
(a) In a series of games, what is the probability that the first time he fails to score a goal is on
his fifth penalty kick?
(b) What is the probability that he scores on 5 or fewer of his next 10 penalty kicks?