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deviation of $25. If the management wants to give free gifts to at most 11.51% of the customers, what should the amount be above which a customer would receive a free gift?

deviation of $25. If the management wants to give free gifts to at most 11.51% of the customers, what should the amount be above which a customer would receive a free gift?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 $25. If the management wants to give free gifts to at most 11.51% 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.** **Explanation:** To solve this problem, you need to determine the cutoff value for the expenditure above which only 11.51% of customers fall. This involves finding the corresponding z-score for the 88.49th percentile (since 100% - 11.51% = 88.49%) and then using the mean and standard deviation to convert this z-score into a dollar amount.
Transcribed Image Text: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 $25. If the management wants to give free gifts to at most 11.51% 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.** **Explanation:** To solve this problem, you need to determine the cutoff value for the expenditure above which only 11.51% of customers fall. This involves finding the corresponding z-score for the 88.49th percentile (since 100% - 11.51% = 88.49%) and then using the mean and standard deviation to convert this z-score into a dollar amount.
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