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An elevator has a placard stating that the maximum capacity is 1256 lb for 8 passengers. So, 8 adult male passengers can have a mean weight of up to [tex]\frac{1256}{8} = 157[/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 157 lb.

Assume that weights of males are normally distributed with a mean of 164 lb and a standard deviation of 28 lb.

Does this elevator appear to be safe?

The probability that the elevator is overloaded is ___.

Answer :

Final answer:

The probability that the elevator is overloaded is approximately 0.6064 or 60.64%.

Explanation:

To find the probability that the elevator is overloaded, we need to determine the probability that the mean weight of 8 passengers is greater than 157 lb.

We can use the Central Limit Theorem to approximate the distribution of the mean weight. The mean weight of 8 passengers is normally distributed with a mean of 164 lb and a standard deviation of 28 lb divided by the square root of 8 (since we're taking the mean of a sample size of 8).

By z-scoring the value of 157, we can find the corresponding area under the normal curve, which represents the probability that the mean weight is greater than 157 lb. Using a standard normal distribution table or a calculator, we find that the area to the right of the z-score is approximately 0.6064. Therefore, the probability that the elevator is overloaded is approximately 0.6064 or 60.64%.

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