Remember: Probabilities and proportions are expressed in %, to 2 decimal places. Use 4 decimal places and round to 2 places. I Fifty percent of Americans believed the country was in recession even though no two quarters had been observed in the economy in a row with negative growth. (BusinessWeek, July 30, 2001). Given a sample of 20 Americans, calculate the following. (10 sts) a) Calculate the probability that exactly 12 people have believed the country was in recession. (2 sts.) b) Calculate the probability that at least five people believed the country was in recession. (2 sts.) c) How many people would you expect to say the country was in recession? (2 sts.) d) Calculate the variance in the number of people who believed the country was in recession. (2 sts.) e) Calculate the standard deviation from the number of people who believed the country was in recession. (2 sts.)