Problem 1. In July 2001, 45% of Americans believed the country was

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

for full credit.

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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?