PSTAT 109: Quiz 6 Winter 2014

PSTAT 109: Quiz 6

Winter 2014

Instructions: Please show all formulas and calculations in an organized fashion

for full credit.

Problem 1. In July 2001, 45% of Americans believed the country was in a recession even

though, technically, the economy had not shown two straight quarters of negative growth.

For a sample of 20 Americans, make the following calculations (assume each person's belief

in recession is independent of the others):

a. Compute the probability that exactly 12 people believed the country was in a recession.

b. Compute the probability that at least one person believed the country was in a reces-

sion.

c. How many people would you expect to say the country was in a recession?

d. Compute the variance and standard deviation of the number of people who believed

the country was in a recession.

Problem 2. Let W denote a random variable that has a Poisson distribution with mean

 = 2. Find

a. P(W = 2),

b. P(W  3), and

c. P(W  3jW  1).

Problem 3. The New York Times reported that the mean time to download the IRS home-

page is 0.8 seconds. Suppose that the download time is normally distributed with a standard

deviation of 0.2 seconds.

a. What is the probability that a download time is less than 1 second?

b. What is the probability that a download time is between 0.5 and 1.5 seconds?