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An elevator has a placard stating that the maximum capacity is 1570 lb for 10 passengers. Thus, 10 adult male passengers can have a mean weight of up to [tex]\frac{1570}{10} = 157[/tex] pounds.

If the elevator is loaded with 10 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 157 lb. Assume that weights of males are normally distributed with a mean of 162 lb and a standard deviation of 27 lb.

Does this elevator appear to be safe?

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

2. Does this elevator appear to be safe?
A. No, there is a good chance that 10 randomly selected adult male passengers will exceed the elevator capacity.
B. Yes, 10 randomly selected adult male passengers will always be under the weight limit.
C. No, 10 randomly selected people will never be under the weight limit.
D. Yes, there is a good chance that 10 randomly selected people will not exceed the elevator capacity.

Answer :

The probability that the elevator is overloaded because 10 adult male passengers have a mean weight greater than 157 lb is 0.2257. This indicates that there is a good chance that the elevator will exceed its capacity. Therefore, the elevator does not appear to be safe.

To determine the probability of the elevator being overloaded, we need to consider the distribution of the mean weight of 10 adult male passengers. Since we are given that the weights of males are normally distributed with a mean of 162 lb and a standard deviation of 27 lb, we can use these parameters to calculate the probability.

The mean weight of 10 adult male passengers can be calculated by dividing the maximum capacity of the elevator (1570 lb) by the number of passengers (10), which gives us a mean weight of 157 lb.

Next, we need to calculate the standard deviation of the mean weight. Since we are dealing with a sample of 10 passengers, the standard deviation of the sample mean can be calculated by dividing the standard deviation of the population (27 lb) by the square root of the sample size (√10). This gives us a standard deviation of approximately 8.544 lb.

Now, we can use the normal distribution to find the probability that the mean weight of 10 adult male passengers is greater than 157 lb. We need to calculate the z-score, which represents the number of standard deviations away from the mean. The z-score is calculated by subtracting the mean weight (157 lb) from the population mean (162 lb) and dividing it by the standard deviation of the sample mean (8.544 lb).

z = (162 - 157) / 8.544 ≈ 0.5867

Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of 0.5867, which is approximately 0.2257.

This means that there is a 22.57% probability that the mean weight of 10 randomly selected adult male passengers will exceed the weight limit of the elevator. Therefore, the elevator does not appear to be safe, as there is a significant chance of it being overloaded under these conditions.

To learn more about probability visit : https://brainly.com/question/13604758

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