Question

An elevator has a placard stating that the maximum capacity is 1312 lb—8 passengers. So, 8 adult male passengers can have a mean weight of up to 1312 / 8 = 164 pounds. If

the elevator is loaded with 8 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 164 lb. (Assume that weights Of
males are normally distributed with a mean of 166 lb and a standard deviation of 35 lb.) Does this elevator appear to be safe?

Answer 1

The student's question deals with calculating the probability of an elevator being overloaded using the normal distribution. Since the actual mean weight of males is higher than the safe limit, there's a considerable risk that the elevator might be unsafe.

Step-by-step explanation:

The student is asking about finding the probability that an elevator is overloaded with eight adult male passengers, given that the weights of adult males are normally distributed. To solve this, we need to use the standard normal distribution because we have a sample mean rather than just a single individual's weight. Here are the steps:

1. First, calculate the standard error of the mean, which is the standard deviation divided by the square root of the sample size (35 lb / √8).
2. Next, find the z-score that corresponds to a mean weight of 164 lb.
3. Use the standard normal distribution to find the probability that the mean is greater than this z-score.

In this case, since the mean weight of adult males is 166 lb, which is already higher than the maximum mean weight allowed for safety (164 lb), there is a significant probability that the elevator could be overloaded, suggesting that the elevator might not be safe under these assumptions.