An elevator has a placard stating that the maximum capacity is 2595 lb-15 passen

Question

An elevator has a placard stating that the maximum capacity is 2595 lb-15 passengers. So, 15 adult male passengers can have a mean weight of up to 2595/15- 173 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 173 lb. (Assume that weights of males are normally distributed with a mean of 180 lb and a standard deviation of 31 lb.) Does this elevator appear to be safe? The probability the elevator is overloaded is (Round to four decimal places as needed.)

Explanation / Answer

From central limit theorem,

Mean of n random variables from a normal distribution are normally distributed with the mean = population mean and standard deviation = (Sigma) / square root(n)

standard deviation = 31 / square root(15) = 8.00416558216

Z for 173 is (173-180)/8.00416558216 = -0.87454462656

P ( Z > -0.87454462656) = 0.8090

Thus, the probability that the elevator is overloaded is 0.8090

( for finding this, you can use the formula in excel : = 1- NORM.S.DIST(-0.874544,TRUE)

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