Elevator Safety Exercise 1 uses μ = 182.9 lb, which is based on Data Set 1. Repeat Exercise 11 using μ = 174 lb (instead of 182.9 lb), which is the assumed mean weight that was commonly used just a few years ago. Assuming that the mean weight of males is now 182.9 lb, not the value of 174 lb that was used just a few years ago, what do you conclude about the effect of using an outdated mean that is substantially lower than it should be?

Exercise 1

Elevator Safety referred to an Ohio elevator with a maximum capacity of 2500 lb. When rating elevators, it is common to use a 25% safety factor, so the elevator should actually be able to carry a load that is 25% greater than the stated limit. The maximum capacity of 2500 lb becomes 3125 lb after it is increased by 25%, so 16 male passengers can have a mean weight of up to 195.3 lb. If the elevator is loaded with 16 male passengers, find the probability that it is overloaded because they have a mean weight greater than 195.3 lb. (As in Example 1, assume that weights of males are normally distributed with a mean of 182.9 lb and a standard deviation of 40.8 lb.) Does this elevator appear to be safe?

Example 1 Designing Elevators

Answer :

Step 1 of 1 :

Elevator Safety Exercise 1 uses μ = 182.9 lb, which is based on Data Set 1. Repeat Exercise 11 using μ = 174 lb (instead of 182.9 lb), which is the assumed mean weight that was commonly used just a few years ago. Assuming that the mean weight of males is now 182.9 lb, not the value of 174 lb that was used just a few years ago.

By the central limit theorem,the sample mean is normally distributed with mean and standard deviation .

The elevator is loaded with 16 male passengers,a mean weight of up to 195.3 lb.

Here n = 16 and x=195.3

We assume that the mean weight of males is now 182.9 lb, not the value of 174 lb that was used just a few years ago.and a standard deviation of 40.8 lb.

So standard deviation = 40.8 and mean = 174

The z-score is the value decreased...