Question

A boat capsized and sank in a lake. Based on an assumption of a mean weight of 130 lb, the boat was rated to carry 60 passengers (so the load limit was 7,800 lb). After the boat sank, the assumed mean weight for similar boats was changed from 130 lb to 171 lb.

The probability is
A. Assume that a similar boat is loaded with 60 passengers, and assume that the weights of people are normally distributed with a mean of 178.3 lb and a standard deviation of 39.1 lb. Find the probability that the boat is overloaded because the 60 passengers have a mean weight greater than 130 lb.
B. The boat was later rated to carry only 16 passengers, and the load limit was changed to 2,736 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 171 (so that their total weight is greater than the maximum capacity of 2,736 lb).

Answer 1

This mathematics question entails calculating the probability of a boat being overloaded based on the mean weight of passengers assuming a normal distribution.

Step-by-step explanation:

The task is to calculate the probability of an event occurring when weights are normally distributed. For part A, we would calculate the probability that the mean weight of 60 passengers exceeds 130 lb using the provided mean of 178.3 lb and standard deviation of 39.1 lb. In part B, we determine the probability that the mean weight of 16 passengers exceeds 171 lb so that their total weight is more than the load limit of 2,736 lb.