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Answer :
The probability that the elevator is overloaded because the mean weight of 8 adult male passengers exceeds 173 lb can be determined by calculating the z-score and finding the corresponding probability using the standard normal distribution.
To calculate the probability that the elevator is overloaded because the mean weight of 8 adult male passengers exceeds 173 lb:
Step 1: Calculate the mean weight of 8 adult male passengers:
Mean weight = 180 lb (given)
Step 2: Calculate the standard deviation of the sampling distribution of the mean:
Standard deviation of individual weights = 29 lb (given)
Sample size = 8
Standard deviation of the sampling distribution of the mean = Standard deviation of individual weights / √(sample size)
= 29 / √8
Step 3: Calculate the z-score:
Z-score = (Mean weight - Population mean) / Standard deviation of the sampling distribution of the mean
Z-score = (173 - 180) / (29 / √8)
Step 4: Find the probability corresponding to the z-score:
Using the standard normal distribution table or a statistical software, find the probability associated with the calculated z-score.
Therefore, by calculating the z-score and finding the corresponding probability, we can determine the probability that the elevator is overloaded because the mean weight of 8 adult male passengers exceeds 173 lb. If the probability is high, it indicates a higher risk of overload.
To know more about probability, visit:
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