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Answer :
find the probability that the elevator is overloaded, we need to calculate the probability that the mean weight of 12 adult male passengers is greater than 172 lb. Looking up the z-score of -0.102 in the z-table gives us a probability of 0.4599.
The probability is calculated using the z-score and the Central Limit Theorem. The elevator appears to be safe as the probability of the mean weight being greater than 172 lb is below the threshold.
To find the probability that the elevator is overloaded, we need to calculate the probability that the mean weight of 12 adult male passengers is greater than 172 lb.
ince the weights of males are normally distributed with a mean of 175 lb and a standard deviation of 34 lb, we can use the Central Limit Theorem to approximate the distribution of the mean weight.
We can calculate the z-score for a mean weight of 172 lb and then use the z-table to find the probability of getting a z-score greater than that.
If the probability is less than a pre-determined threshold, the elevator is considered safe.
The formula to calculate the z-score is: z = (x - µ) / (σ / sqrt(n)). Here,
x = 172 lb,
µ = 175 lb,
σ = 34 lb,
and n = 12.
Substituting these values into the formula gives us: z = (172 - 175) / (34 / sqrt(12))
= -1 / 9.795
= -0.102.
Looking up the z-score of -0.102 in the z-table gives us a probability of 0.4599.
This means that there is a 45.99% chance that the mean weight of 12 adult male passengers is greater than 172 lb. Since this probability is greater than the threshold for being considered safe, the elevator appears to be safe.
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