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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