Elevator Safety Example 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, 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 Designing Elevators

Answer :

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Elevator Safety Example 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.

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 weights of males are normally distributed with a mean of 182.9 lb and a standard deviation of 40.8 lb.

So = 40.8 and mean = 182.9

Now we have to find the probability that it is overloaded because they have a...