An elevator has a placard stating that the maximum capacity is 19201920 lblong dash—1212 passengers. so, 1212 adult male passengers can have a mean weight of up to 1920 divided by 12 equals 160 pounds.1920/12=160 pounds. if the elevator is loaded with 1212 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 160160 lb. (assume that weights of males are normally distributed with a mean of 163 lb163 lb and a standard deviation of 29 lb29 lb.) does this elevator appear to be safe?

This means that there is a 1-0.3594 = 0.6406 = 64.06% probability that the elevator is overloaded. This a good chance that the elevator's limit weight will be exceeded. So, this elevator does not appear to be safe.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

In this problem, we have that:

Assume that weights of males are normally distributed with a mean of 163 lb and a standard deviation of 29 lb.

This means that .

We have a sample of 12 adults, and we want to calculate the zscore of THE SAMPLE'S AVERAGE so we need to find the standard deviation of the sample. This is

Find the probability that it is overloaded because they have a mean weight greater than 160.

This is 1 subtracted by the pvalue of Z when

has a pvalue of 0.3594.

This means that there is a 1-0.3594 = 0.6406 = 64.06% probability that the elevator is overloaded. This a good chance that the elevator's limit weight will be exceeded. So, this elevator does not appear to be safe.

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