Question

an elevator has a placard stating that the maximum capacity is 1944 lbs- 12 passengers. So, 12 adult male passengers can have a mean weight of up to 1944/12 =162 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 162 lbs. (Assume that weights are normally distributed with a mean of 166 lb and a standard deviation of 33 lb.) Does the elevator appear to be safe

Answer 1

Y=sample mean based on 12 passengers

Then Y~N(166,SD=)

P(the lift is overloaded)=P(Y>162)= 0.6627175

The probability of overloading is about 66%. That is in 66% cases, it will indicated overloading when there is actually overloading and in 34% cases it will not show overloading when actually there is overloading. Ideally a safe elevator should indicate overloading most of the  the times, whenever mean weight exceeds 162. Thus the elevator does not seem to be safe.