Question

An elevator has a placard stating that the maximum capacity is 2100 lblong dash 12 passengers.​ So, 12 adult male passengers can have a mean weight of up to 2100 divided by 12 equals 175 pounds. If the elevator is loaded with 12 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 175 lb.​ (Assume that weights of males are normally distributed with a mean of 179 lb and a standard deviation of 26 lb ​.) The probability the elevator is overloaded is ?

Answer 1

Assume that weights of males are normally distributed with a mean of 179 lb and a standard deviation of 26 lb ​.

Let X be the weight of any given male. X is normally distributed with mean and standard deviation

Let be the mean weight of a randomly selected sample of n=12 males. Although the sample size is less than 30, we know the population standard deviation. Hence using the central limit theorem, we can say that is normally distributed with mean and standard deviation (also called the standard error of mean)

the probability that the elevator is overloaded because the group of 12 males have a mean weight greater than 175 lb is

ans: The probability the elevator is overloaded is 0.7019