An elevator has a placard stating that the maximum capacity is 1384 lb for 8 passengers. Therefore, 8 adult male passengers can have a mean weight of up to [tex]\frac{1384}{8} = 173[/tex] 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 173 lb. (Assume that weights of males are normally distributed with a mean of 180 lb and a standard deviation of 29 lb.)

Does this elevator appear to be safe?

The probability that the elevator is overloaded is _______.

The probability that the elevator is overloaded because the mean weight of 8 adult male passengers exceeds 173 lb can be determined by calculating the z-score and finding the corresponding probability using the standard normal distribution.

To calculate the probability that the elevator is overloaded because the mean weight of 8 adult male passengers exceeds 173 lb:

Step 1: Calculate the mean weight of 8 adult male passengers:

Mean weight = 180 lb (given)

Step 2: Calculate the standard deviation of the sampling distribution of the mean:

Standard deviation of individual weights = 29 lb (given)

Sample size = 8

Standard deviation of the sampling distribution of the mean = Standard deviation of individual weights / √(sample size)

= 29 / √8

Step 3: Calculate the z-score:

Z-score = (Mean weight - Population mean) / Standard deviation of the sampling distribution of the mean

Z-score = (173 - 180) / (29 / √8)

Step 4: Find the probability corresponding to the z-score:

Using the standard normal distribution table or a statistical software, find the probability associated with the calculated z-score.

Therefore, by calculating the z-score and finding the corresponding probability, we can determine the probability that the elevator is overloaded because the mean weight of 8 adult male passengers exceeds 173 lb. If the probability is high, it indicates a higher risk of overload.

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