The management of a supermarket wants to adopt a new pro- motional policy of giv

Question

The management of a supermarket wants to adopt a new pro- motional 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 adver- tised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. If the management decides to give free gifts to all those customers who spend more than $130 at this supermarket during a visit, what percentage of the customers are expected to receive free gifts?

Explanation / Answer

as we know for normal distribution ; zscore =(X-mean)/std deviation

therefore probability of the customers are expected to receive free gifts =P(X>130)

=1-P(X<130)=1-P(Z<(130-95)/20)=1-P(Z<1.75)=1-0.9599=0.0401

hence percentage of the customers are expected to receive free gifts =4.01%

please revert for any clarification needed.

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