The management of a supermarket wants to adopt a new promotional policy of givin

Question

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 $80 and a standard deviation of $40.82. If the management decides to give free gifts to all those customers who spend more than $100 at this supermarket during a visit, what percentage of the customers are expected to get free gifts? Round your answer to two decimal places. % of the customers are expected to get free gifts.

Explanation / Answer

Mean = 68
Stdev = 40.82

We normalize using the params of normal distribution as follows:

P(X>100)

= P(Z> (100-80)/40.82 )

= P(Z>.49)

= .6879

or 68.79% of people will get free gifts

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