Chapter 06, Section 6.4, Problem 041 The management of a supermarket wants to ad

Question

Chapter 06, Section 6.4, Problem 041 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 $100 and a standard deviation of $23. If the management wants to give free gifts to at most 15.39% 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 S to receive a free gift. the tolerance is +/-2%

Explanation / Answer

the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 100
standard Deviation ( sd )= 23
P ( Z > x ) = 0.1539
Value of z to the cumulative probability of 0.1539 from normal table is 1.0198
P( x-u / (s.d) > x - 100/23) = 0.1539
That is, ( x - 100/23) = 1.0198
--> x = 1.0198 * 23+100 = 123.4565
a customer should spend atleast 123.46$ to receive a gift

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