An elevator has a placard stating that the maximum capacity is 2625 lb— 15 passengers.​

Question

So, 15 adult male passengers can have a mean weight of up to 2625 / 15 =175 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 175 lb.​ (Assume that weights of males are normally distributed with a mean of 177 lb and a standard deviation of 33 lb​.) Does this elevator appear to be​ safe?

The probability the elevator is overloaded is ...

Answer 1

Hi Sabrina, you'll want to calculate the standard error, then use that to calculate the probability that a normally distributed random variable with mean 177 and standard deviation 33 is greater than 175.

The standard error is σ / \sqrt(n) = 33 / sqrt(15), about 8.52 lbs.

And you can calculate the probability using a probability calculator, like the one at geogebra "dot" org "backslash" classic "hashtag" probability. With μ = 177, σ = 8.52, find P(175 < X).