SOLUTION: An elevator has a placard stating that the maximum capacity is 1590 lblong dash10 passengers.​ So, 10 adult male passengers can have a mean weight of up to 1590 divided by 10 equ

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Question 1135429: An elevator has a placard stating that the maximum capacity is 1590 lblong dash10 passengers.​ So, 10 adult male passengers can have a mean weight of up to 1590 divided by 10 equals 159 pounds. If the elevator is loaded with 10 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 159 lb.​ (Assume that weights of males are normally distributed with a mean of 168 lb and a standard deviation of 34 lb​.) Does this elevator appear to be​ safe?

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
That probability uses z>=(x bar-mean)/sigma/sqrt(n)
z>=(159-168)/34/sqrt(10)
this is z>=-9*sqrt(10)/34, which is z>=-0.84
This has probability 0.7995
One can't say whether or not it is safe; one may say that with high probability, ten normal men would have a mean weight exceeding the maximum capacity. It would be up to engineers to say with that information whether the elevator itself would be safe.