help with a problem and is there any way to check my answer so i am not double guessing?
An elevator has a stated maximum capacity of 12 people or 2004 pounds. If 12 people have weights with a mean greater than (2004/12) = 167 pounds, the capacity will be exceeded. Assume that weights of men are normally distributed with a mean of 182.9 pounds and a standard deviation of 40.8 pounds. Show your work and round your answers to FOUR decimal places.
a. Compute the probability that a randomly selected man will have a weight greater than 167 pounds.
b. Compute the probability that 12 randomly selected men will have a mean weight that is greater than 167 pounds.
c. Does the elevator appear to have the correct weight limit? Why or why not?
mean = 182.9 SD = 40.8
a. z(167)=(167-182.9)/40.8=-0.389706 or -0.3897
p(z>-0.3897)=0.3520.....using the z score table
b. z= (169-182.9)/[40.8/√(12)] = -1.180172 or -1.1802
c. No there is a good chance that 12 randomly selected people will exceed the elevator capacity.
How could i check my work so that I know I was on the right track because I think I did this correctly but I could be wrong.