The management of a supermarket wants to adopt a new promoti

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of dollar-sign 115 and a standard deviation of dollar-sign 21. If the management wants to give free gifts to at most 11.12% of the customers, what should the amount be above which a customer would receive a free gift?

Solution

Mean ( u ) =115
Standard Deviation ( sd )=21
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z > x ) = 0.1112
Value of z to the cumulative probability of 0.1112 from normal table is 1.22
P( x-u/ (s.d) > x - 115/21) = 0.1112
That is, ( x - 115/21) = 1.22
--> x = 1.22 * 21+115 = 140.62 ~ 141