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

Normal Distribution
Mean ( u ) =100
Standard Deviation ( sd )=30
Normal Distribution = Z= X- u / sd ~ N(0,1)
The total will be more than $5100 when the sample average exceeds= 5100/50 = 102              
P(X > 102) = (102-100)/30
= 2/30 = 0.0667
= P ( Z >0.067) From Standard Normal Table
= 0.4734