Reference no: EM132153567

1. The Ethan Allen tour boat capsized and sank in Lake George, New York, and 20 of the 47 passengers drowned. Based on a 1960 assumption of a mean weight of 140 lb. for passengers, the boat was rated to carry 50 passengers. After the boat sank, New York changed the assumed mean weight from 140 lb. to 170 lb.

(a) Given that the boat was rated for 50 passengers with an assumed mean of 140 lb, the boat had a passenger limit of 7000 lb. Assume that the boat is loaded with 50 male passengers and assume the weights of men are normally distributed with a mean weight of 182.9 lb. and a standard deviation of 40.8 lb. Find the probability that the 50 passengers have a mean weight greater than 140 lb.

(b) The boat was later rated to carry only 14 passengers and the load limit was changed to 2436 lb. Assume the weights of men are normally distributed with a mean weight of 182.9 lb and a standard deviation of 40.8 lb. If 14 passengers are all male,  find the probability that their mean weight is greater than 174 lb. This would mean that their total weight is greater than the maximum capacity of 2436 lb. Do the new ratings appear to be safe when the boat is loaded with 14 male passengers?

2. A survey by Harris Interactive reported that 35% of college students prefer digital textbooks over traditional print textbooks. State University would like to confirm these results.

A random sample of 125 students was asked their textbook preference and a total of 37 preferred the digital format. Use a 95% confidence interval to validate the Harris Interactive findings.