Central Limit Theorem

KC1

New Member
#1
I am having trouble coming up with the right answer for the following problem:

Elevator Design: Womens heights are normally distributed with a mean of 143 lbs and a standard deviation of 29 lbs, and men's weights are normally distributed with a mean of 172 lbs and a standard deviation of 29 lbs. You need to design an elevator for the westport shopping center, and it must safely carry 16 people. Assuming a worst case scenario of 16 male passengers, find the maximum total allowable weight if we want a .975 probability that this maximum will not be exceeded when 16 males are randomly selected.

Men: mean of 172, standard deviation 29, probability .975 = 1.96 z from the chart.

I used the formula to find x: 172 + (1.96 x 29) = 228.84 x 16 = 3661 lbs

The book came up with 2979 lbs

What am I doing wrong??

Thank you
KC1
 

JohnM

TS Contributor
#2
The standard deviation of the total weight of 16 people will not be s = 29.

The mean of a total of 16 will be 172 * 16 = 2752.

The std dev of this total will be the square root of (variance * 16).