Answer :
The probability that the elevator is overloaded due to the mean weight of the 10 adult male passengers being greater than 172 lb is approximately 0.834. This indicates that the elevator may not be safe to carry 10 adult male passengers with a mean weight greater than 172 lb.
To find the probability that the elevator is overloaded due to the mean weight of the 10 adult male passengers being greater than 172 lb, we can use the concept of the sampling distribution of the sample mean.
The mean weight of the 10 adult male passengers is normally distributed with a mean of 180 lb and a standard deviation of 26 lb.
To calculate the probability, we need to find the probability of obtaining a sample mean greater than 172 lb from this distribution.
First, we need to calculate the standard error of the mean (SE) which is the standard deviation of the population divided by the square root of the sample size:
SE = 26 / √10 ≈ 8.227
Next, we can convert the sample mean to a z-score using the formula:
z = (sample mean - population mean) / SE
z = (172 - 180) / 8.227 ≈ -0.971
Using a standard normal distribution table or a statistical software, we can find the probability of obtaining a z-score greater than -0.971.
The probability is approximately 0.834 (rounded to four decimal places).
Therefore, the probability that the elevator is overloaded due to the mean weight of the 10 adult male passengers being greater than 172 lb is 0.834.
As the probability of the elevator being overloaded is quite high, it suggests that the elevator may not be safe to carry 10 adult male passengers with a mean weight greater than 172 lb.
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