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Answer :
Using the standard normal distribution formula, it is calculated that there is approximately a 59.87% chance that the elevator will be overloaded with 15 adult males, suggesting it might not be safe.
To answer whether the elevator is likely to be overloaded if there are 15 adult male passengers onboard, you'll need to calculate the probability that the mean weight of these men exceeds the maximum capacity per person, which has been calculated as 174 lb.
Given that the weights of males are normally distributed with a mean of 176 lb and a standard deviation of 31 lb, the probability can be determined using the standard normal distribution formula (Z = (X - μ) / σ).
Here, X is the weight to be checked (174 lb), μ is the mean weight (176 lb), and σ is the standard deviation (31 lb).
Before proceeding, however, note that we are considering the mean weight of 15 men, not an individual's weight.
So, the standard deviation for the mean of 15 men will decrease, being equal to σ / sqrt(n), where n equals the number of observations.
In our case, n=15. So, the new standard deviation will be 31 / sqrt(15), which is approximately 8 lb.
Now, apply these values to the Z formula: Z = (174 - 176) / 8, which results in a Z-score of -0.25.
Looking up this Z-score in a standard normal distribution table provides a probability of about 0.4013.
However, since we are looking for the probability of weight being above 174 lb (greater mean), the probability will be 1 - 0.4013 = 0.5987 (or 59.87%) for the elevator to be overloaded.
Thus, based on these calculations, it appears that the elevator may not be safe, as there is a fairly high probability (59.87%) that 15 adult males would overload it.
Learn more about Probability here:
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