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?
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