Statistics Probability Question

Question

An elevator has a placard stating that the maximum capacity is 2475 lb-15 passengers. So, 15 adult male passengers can have a mean weight of up to 2475/15= 165 lbs. If the elevator is loaded with 15 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 165 lb. (Assume that weights of males are normally distributed with a mean of

168 lb and a standard deviation of 31 lb.)

What is the probability the elevator was overloaded? Round to FOUR decimal places.

We are allowed to use excel to solve this, but I don't know what formula/order to use. Please help! Thanks.

Answer 1

Hello -

If the values in the stated problem are correct, the answer is a little scary...

Since we are dealing with a distribution of a Mean, we need to find the standard deviation of the mean.

The formula is: std dev of mean = (std dev)/sqrt(n) = 31/sqrt(15) = 8.00

Then calculate the Z score for x bar = 165...

(x bar - mean)/std dev of mean = (165-168)/8 = -0.375

Looking up the Probability in the Z chart for -.0375 gives P(x < -0.375)= .3538

Since we are interested in the probability x>165, we have to subtract the above result from 1

1- 0.3538 = 0.6462

Probability the elevator will be overloaded = 0.6462 (64.62%)

While this sounds like a high percentage, it is not a surprising result given the mean weight of males is stated to be 168 lbs, 3 lbs higher that the maximum average weight of 165 to not overload the elevator.

I hope that helps!