Final answer:
To find the probability that the elevator is overloaded because the mean weight of 8 adult male passengers is greater than 156 pounds, we calculate the z-score and find the probability using a standard normal distribution table or a calculator.
Step-by-step explanation:
To find the probability that the elevator is overloaded because the mean weight of 8 adult male passengers is greater than 156 pounds, we need to calculate the probability of the mean weight being greater than 156 pounds. Since the weights of males are normally distributed with a mean of 166 pounds and a standard deviation of 29 pounds, we can use the standard deviation formula to calculate the standard error of the mean. The standard error of the mean, or standard deviation divided by the square root of the sample size, in this case, would be 29/√8. We can then calculate the z-score using the formula: (156 - 166) / (29/√8). With the z-score, we can find the probability using a standard normal distribution table or a calculator. The probability that the elevator is overloaded is the probability of the z-score being greater than the calculated z-score.
Assuming that the weights of males are normally distributed with a mean of 166 pounds and a standard deviation of 29 pounds, the probability that the elevator is overloaded because the mean weight of 8 adult male passengers is greater than 156 pounds is approximately 0.8849 (rounded to four decimal places).
The elevator does not appear to be safe since there is a high probability that it will be overloaded with 8 adult male passengers.