Question 1121957
mean is 100,000
standard deviation is 8,000
you are looking for the operating costs that are greater than 90% of the operating costs.
they would be in the top 10%.
find the z-score where 90% of the area under the normal distribution curve is to the left of it.
that z-score will be 1.281551567 according to my TI-84 Plus calculator.
use the z-score formula to find the raw score associated with that.
the formula is z = (x - m) / s
z is the z-score
x is the raw score
m is the mean
s is the standard deviation.
that formula becomes:
1.281551567 = (x - 100,000) / 8,000.
solve for x to get x = 1.281551567 * 8,000 + 100,000 = 110,252.4125.
round that to the nearest thousand and provide it in thousands of dollars and the answer is 110.


to confirm, i used the following online calculator.


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


the calculator confirmed that 10% of the operating costs were above 110,252.4.


here's the what the calculator output looked like.


<img src = "http://theo.x10hosting.com/2018/082805.jpg" alt="$$$" >


bottom line:


your answer should be 110.