SOLUTION: An elevator has a placard stating that the maximum capacity is 2370 lb/15 passengers.​ So, 15 adult male passengers can have a mean weight of up to 2370 divided by 15 equals

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Question 1125245: An elevator has a placard stating that the maximum capacity is 2370 lb/15 passengers.​ So, 15 adult male passengers can have a mean weight of up to 2370 divided by 15 equals 158 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 158 lb.​ (Assume that weights of males are normally distributed with a mean of 162 lb and a standard deviation of 28 lb​.) Does this elevator appear to be​ safe?
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
z=(xbar-mean)/sigma/sqrt(n)
=(158-162)/28/sqrt(15)
=-4/7.23
z>-0.55, which has a probability being overloaded of 0.7088
Samples of 15 men have an average weight of 162 with a sd of 7.23
Therefore, it is more likely than not that an elevator with 15 men will be overloaded.

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