Q1) Water taxi recently sank in Baltimore's Inner Harbor. Among 25 people on board, 5 died and 16 were injured.

Investigation disclosed that safe passenger load for water taxi was 3500 pounds. Suppose a mean passenger weight of 140 pounds, boat was permitted to carry 25 passengers, but mean of 140 pounds was determined 44 years ago when people were not as heavy as they are today. (Sample mean weight of 25 passengers aboard boat that sank was found to be 168 pounds)

National transportation and safety board suggested that old estimated mean of 140 pounds be updated to 174 pounds, so safe load of 3500 pounds would now permit only 20 passengers instead of 25.

Suppose a "worst case" scenario in which all of passengers are adult men. (This could easily happen in city which hosts conventions in which people of same gender often travel in groups) Based on data from National Health and Nutrition Examination Survey, suppose that weights of men now are normally distributed with mean of m =172 pounds and standard deviation of s = 29 pounds.

If one man is arbitrarily selected, determine the probability that he weighs less than 174 pounds ( 'safe' value suggested by National transportation and safety board).

a) Determine the probability that if the individual man is arbitrarily selected, his weight will be greater than 175 pounds.

b) Determine the probability that 20 arbitrarily selected men will have mean that is greater than 175 pounds (so that their total weight exceeds safe capacity of 3500 pounds).

c) What weight separates lightest 99.5% of men from the heaviest 0.5%?