Final answer:
To find the probability that the elevator is overloaded with 12 adult male passengers whose mean weight is greater than 159 pounds, we need to calculate the probability using the Central Limit Theorem. The resulting probability is approximately 0.835. This elevator does not appear to be safe.
Step-by-step explanation:
To find the probability that the elevator is overloaded, we need to calculate the probability that the mean weight of the 12 adult male passengers is greater than 159 pounds. We know that the weights of males are normally distributed with a mean of 167 pounds and a standard deviation of 29 pounds.
Using the Central Limit Theorem, we can treat the sample mean as a normally distributed random variable. The mean of the sample mean is equal to the population mean, which is 167 pounds. The standard deviation of the sample mean is equal to the population standard deviation divided by the square root of the sample size, which is 29 pounds divided by the square root of 12.
Next, we need to standardize the sample mean to calculate the probability. The z-score formula is z = (sample mean - population mean) / (standard deviation of the sample mean). Plugging in the values, we get z = (159 - 167) / (29 / sqrt(12)).
Finally, we can use a z-table or a statistical calculator to find the probability of z > -0.972. This probability corresponds to the area under the standard normal curve to the right of -0.972. The resulting probability is approximately 0.835.
Therefore, the probability that the elevator is overloaded because the mean weight of the 12 adult male passengers is greater than 159 pounds is approximately 0.835.
This elevator does not appear to be safe as there is a high probability of being overloaded.