PSTAT 109: Quiz 6 Winter 2014

PSTAT 109: Quiz 6 Winter 2014

Question
	
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.LetWdenote a random variable that has a Poisson distribution with mean

= 2. Find

a.P(W= 2),

b.P(W3), and

c.P(W3jW1).

Problem 3.TheNew York Timesreported 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?