An elevator has a placard stating that the maximum capacity is 2355 pounds for 15 passengers. So, 15 adult male passengers can have a mean weight of up to [tex]\frac{2355}{15} = 157[/tex] pounds.

If the elevator is loaded with 15 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 157 pounds. Assume that the weights of males are normally distributed with a mean of 163 pounds and a standard deviation of 27 pounds.

Does this elevator appear to be safe?

The probability that the elevator is overloaded is ___. (Round to four decimal places as needed.)

The elevator has an 88.69% probability of being overloaded with 15 adult males with a mean weight of more than 157 lbs. This is calculated using the Z-score, taking into account the population mean weight and standard deviation. Therefore, the elevator may not be completely safe as its capacity rating puts it at risk of being overloaded.

Explanation:

In order to find the probability that the elevator is overloaded due to passengers with mean weight greater than 157 lbs, we would use the concept of the Z score in statistics. The Z score is used in the field of statistics to help understand how far away a particular data point is from the mean of a distribution.

Here, we're looking for the probability that the mean weight of 15 men exceeds 157 lbs, given that the population mean is 163 lbs and the standard deviation is 27 lbs. The Z score is calculated by the following formula: Z = (X - μ) / (σ / √n), where X is the sample mean (157 lbs), μ is the population mean (163 lbs), σ is the standard deviation (27 lbs), and n is the sample size (15).

Applying the formula, we get Z = (157 - 163) / (27/√15) = -1.21 (rounded to 2 decimal places). Now using the Z score table or any appropriate software for the calculation, you can find that the probability of getting a value less than -1.21 is about 0.1131. That leaves a probability of 1 - 0.1131 = 0.8869 (rounded to 4 decimal points) for the elevator to be overloaded.

Based on this high probability, it appears that this particular elevator's capacity rating, while fitting the average demographic, does put it at risk of being overloaded and is thus, not completely safe.

Learn more about Z score here:

https://brainly.com/question/35667167

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