Activity #6: (9 points) Application of the Central Limit Theorem: Under Federal Aviation Administration rules, airlines are required to estimate the weight of a passenger as 175 pounds. Assume that the population distribution of male weights is Normal with u = 180.5 pounds and o = 32.4 pounds. a. If 1 adult male is randomly selected, find the probability that his weight is greater than 175 pounds. (2 points) b. If a Boeing 767-300 aircraft is full of 150 adult male passengers, find the mean and standard deviation of the sampling distribution of the mean weight of 150 adult male passengers. (3 points) c. Find the probability that the mean weight of the 150 passengers is greater than 175 lb. (2 points) d. Based on your calculations above, should the pilot be worried about exceeding the weight limit? Explain why or why not. (2 points) Activity #7: (7 points) Entrepreneurship. A Gallup survey indicated that 75% of 18 to 29-year olds, given a choice, would prefer to start their own business rather than work for someone else. A random sample of 500 18 to 29-year olds is obtained. a. Describe the sampling distribution (mean and standard deviation) of p, the sample proportion of 18 to 29-year olds who would prefer to start their own business. (3 points) b. In a random sample of 500 18 to 29-year olds, what is the probability that no more than 80% would prefer to start their own business? (2 points) C. Would it be unusual if a random sample of 500 18 to 29-year olds resulted in 250 or less who would prefer to start their own business (remember that unusual is more than 2 standard deviations from the mean? why or why not