Question

An elevator has a placard stating that the maximum capacity is 1610 lb—10 passengers.​ So, 10 adult male passengers can have a mean weight of up to 1610 divided by 10 equals 161 pounds.1610/10=161 pounds. If the elevator is loaded with 10 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 161 lb.​ (Assume that weights of males are normally distributed with a mean of 164 lb and a standard deviation of 29 lb​.) Does this elevator appear to be​ safe?

Answer 1

Given the weights of males are normally distributed with a mean of 164 lb and a standard deviation of 29 lb​.

The mean of weights has distribution .

The probability that it is overloaded because they have a mean weight greater than 161 lb is

This elevator does not appear to be​ safe since probability that it is overloaded is greater than 0.5.