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 of 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?

Your answer should be in decimal form with 4 digits. For example: .4451. When working on the problem remember z scores should have 2 digits after the decimal place. For example, 1.57 or .82. Be sure to use the correct number of digits in your calculations or your final answer will not be correct.

Explanation / Answer

Mean = $95

Standard deviation = $20

P(X < A) = P(Z < (A - mean)/standard deviation)

P(customer expected to get receive free gift) = P(X > 130)

= 1 - P(X < 130)

= 1 - P(Z < (130 - 95)/20)

= 1 - P(Z < 1.75)

= 1 - 0.9599

= 0.0401

Proportion of the customers are expected to receive free gifts = 0.0401

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.