Question

the expenditures for all customers at a supermarket are normally distributed with a mean of $100 and a standard deviation of $30. The store’s management wants to give free coupons to customers who spend in the top 5 percentage of all expenditures. How much will customer have to spend in order to get a coupon?

Answer 1

solution

Using standard normal table,

P(Z > z) = 5%

= 1 - P(Z < z) = 0.05

= P(Z < z ) = 1 - 0.05

= P(Z < z ) = 0.95

= P(Z < 1.64) = 0.95  

z =1.64 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.64*30+100

x= 149.2

x=149