Chapter 06 Section 64 Problem 060 The management of a superm

Chapter 06, Section 6.4, Problem 060

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 $120 and a standard deviation of $18. If the management wants to give free gifts to at most 13.35% of the customers, what should the amount be above which a customer would receive a free gift?

*Round your answer to two decimal places.

A customer should spend at least $ ______ to receive a free gift.

*the absolute tolerance is +/-0.01

Solution

Mean = 120

SD =18

Let S be the amount which customer should spend to receive a free gift

P(Z > (S - 120) / 18) = 0.1335

Reading off a normal table, we have:
(S - 120) / 18 = 1.11
S - 120 = 1.11 * 18
S - 120 = 19.98
S = 120 + 19.98
S = 139.98

Therefore,

$139.98 Answer