The amount of money spent by a customer at a discount store

The amount of money spent by a customer at a discount store has a mean of $100 and a standard deviation of $30. What is the probability that a randomly selected group of 50 shoppers will spend a total of more than $5100? (Hint: The total will be more than $5100 when the sample average exceeds what value?) (Round the answer to four decimal places.)
P(total > 5100) =

Solution

mean=100*50 = 5000

standard deviation = 30*50 =1500

So the probability that a randomly selected group of 50 shoppers will spend a total of more than $5100 is

P(X>5100) = P((X-mean)/s >(5100-5000)/1500)

=P(Z>0.07)=0.4721 (from standard normal table)