Question

A boat capsized and sank in a lake. Based on an assumption of a mean weight of 150 ​lb, the boat was rated to carry 50 passengers​ (so the load limit was 7 comma 500 ​lb). After the boat​ sank, the assumed mean weight for similar boats was changed from 150 lb to 174 lb. Complete parts a and b below. a. Assume that a similar boat is loaded with 50 ​passengers, and assume that the weights of people are normally distributed with a mean of 177.2 lb and a standard deviation of 36.6 lb. Find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 150 lb.

Answer 1

Given:

Mean = = 177.2

Standard deviation = = 36.6

Let X be the weights of people are normally distributed with a mean of 177.2 lb and a standard deviation of 36.6 .

X ~ Normal(=177.2, =36.6)

The probability that the boat is overloaded because the 50 passengers have a mean weight greater than 150 lb :

Therefore the required probability is 1