Passengers died when a water taxi sank in Baltimore’s Inner harbor. Men are typi
ID: 3252013 • Letter: P
Question
Passengers died when a water taxi sank in Baltimore’s Inner harbor. Men are typically heavier than women and children, so when loading a water taxi, assume a worst-case scenario in which all passengers are men. Assume that weights of men are normally distributed with a mean of 182.9 lb and a standard deviation of 40.8 lb. The water taxi that sank has stated capacity of 25 passengers, and the boat was rated for a load limit of 3500 lb.
a. Given that the water taxi that sank was rated for a load limit of 3500 lb, what is the mean weight of passengers if the boat is filled to the stated capacity of 25 passengers?
b. If the water taxi is filled with 25 randomly selected men, what is the probability that their mean weight exceeds that value from part (a)?
Explanation / Answer
a) SInce the boath sank, the mean weight would be greater than/equal to 3500/25=140
Mean weight of 25 men = 25* mean weight of 1 man = 182.9*25=4572
z = (x-mea)/sigma = (4572-3500)/(40.8*sqrt(25))=5.25
P(mean weight exceeds 3500 is 0.9999942