Statistics Question? I'm stuck!?

Weights of Water Taxi Passengers. It was noted in the Chapter Problem that when a water taxi sank in Baltimore's Inner Harbor, an investigation revealed that the safe passenger load for the water taxi was 3500 lb. It was also noted that the mean weight of a passenger was assumed to b 140 lb. Assume a "worst case" scenario in which all of the passengers are adult men. ( This could easily occur in a city that hosts conventions in which people of the same gender often travel in groups.) Based on data from the National Health and Nutrition Examination survey, assume that weights of men are normally distributed with a mean of 172 lb. and a standard deviation of 29lb. a. If one man is randomly selected, find the probability that he weighs less than 174 lb (the new value suggested by the National Transportation and Safety Board). b.With a load limit of 3500 lb, how many men passengers are allowed if we use the new mean weight of 174lb.



I have no idea where to begin and my tutor isn't helpful! Please help me :-)Statistics Question? I'm stuck!?
a)

渭 = 172

蟽 = 29

standardize x to z = (x - 渭) / 蟽

P(x %26lt; 174) = P( z %26lt; (174-172) / 29)

= P(z %26lt; 0.069) =0.5279 -- probability that he weighs less than 174 lb

(From Normal probability table)



b)

3500/174 =20.11 men = 20 men