150 homes randomly selected from a suburb Mean is 2936 SD is

150 homes randomly selected from a suburb. Mean is 2936. SD is 2350. What is the chance that the average monthly water usuage for these 150 homes will exceed 3000 gallons? Put only a number to 4 decimal places. The professor is saying that the answer is 0.3707. I\'m getting 0.4920. I need to know how to work this problem.

Solution

P(xbar>3000) = P((xbar-mean)/(s/vn) >(3000-2936)/(2350/sqrt(150)))

=P(Z>0.33)

=0.3707 (from standard normal table)