An elevator has a placard stating that the maximum capacity is 1296 lb long dash — 8 passengers. so, 8 adult male passengers can have a mean weight of up to 1296 divided by 8 equals 162 pounds. 1296/8=162 pounds. if the elevator is loaded with 8 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 162 lb. (assume that weights of males are normally distributed with a mean of 170 lb and a standard deviation of 29 lb.) does this elevator appear to be safe?

There is a 98.26% probability that it is overloaded.

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 170 lb, so

They have a standard deviation of standard deviation of 29 lb, so .

We have a sample of 8 adults, so we have to find the standard deviation of the sample to use in the place of in the Z score formula.

Find the probability that it is overloaded because they have a mean weight greater than 162 lb, so

has a pvalue 0.0174.

So, there is a 1-0.0174 = 0.9826 = 98.26% probability that it is overloaded.

Any probability that is above 95% is considerer unusually high. So, this elevator does not appear to be safe, since there is a 98.26% probability that it is overloaded.

i need points

step-by-step explanation:

sorry bubs