Probability statistics standard deviation

Question

Men in a certain area have an average weight of 163 pounds with a standard deviation of 27 pounds.

(a) Find the probability that 20 randomly selected men will have a sum weight greater than 3400 lbs. (Round your answer to four decimal places.)

Answer 1

20 men sum weight > 3400 means average weight will exceed 170.

z = (170 - 163)/(27/sqrt(20)) = 1.16

P(xbar > 170) = P(z > 1.16) = 1 - P(z < 1.16) = 1 - .8770 = 0.1230