An elevator has a placard stating that the maximum capacity is 1344 lb—8 passeng

Question

An elevator has a placard stating that the maximum capacity is 1344 lb—8 passengers. So, 88 adult male passengers can have a mean weight of up to 1344 divided by 8 equals 168 pounds.1344/8=168 pounds. If the elevator is loaded with 88 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 168 lb. (Assume that weights of males are normally distributed with a mean of 172 lb and a standard deviation of 31 lb Does this elevator appear to be safe?

Explanation / Answer

P(x>168)

z = (x - mean)/(s/sqrt(n))

= (168 - 172)/(31/sqrt(88))

= -1.2104

P(x>168) = P(z>-1.2104) = 0.8869

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