Question 1084739
the mean is 85
the standard deviation is 25.


you want only the top 10.56% of the customers to receive the gift.


those customers will be the ones who spend a certain amount more than the mean.


you need to find the z-score for an area to the right of that z-score equal to .1056.


subtract .1056 from 1 and you get .8944.


this is the area to the left of that same z-score.


look up in the z-score table, or use a z-score calculator, to find the z-score that has .8944 area under the normal distribution curve to the left of it.


i used a calculator and i got the z-score equal to 1.250272557.


to find the raw score from this z-score, use the z-score formula shown below:


z = (x - m) / s


in this problem:


z = 1.250272557
m = 85
s = 25


you will get 1.250272557 = (x - 85) / 25


solve for x to get x = 25 * 1.250272557 + 85 = 116.2568139


customers who spend more than 116.2568139 dollars will get the free gift.


the percentage of customers who get the gift will be at most 10.56%.


this can be seen visually by using the following online calculator:


<a href = "http://davidmlane.com/hyperstat/z_table.html" target = "_blank">http://davidmlane.com/hyperstat/z_table.html</a>


you would enter the mean as 85 and the standard deviation as 25 and then click on above and enter 116.2568139.


the calculator will tell you that the area above that score is .1056 which is equal to 10.56%.


here's the display.


<img src = "http://theo.x10hosting.com/2017/061404.jpg" alt="$$$" </>