Question 1083845
average is 35,000
standard deviation is 5,000


middle 95% of the normal distribution curve leave 2.5% on each end.


2.5% on each end is your alpha.


z-score is 100% - 2.5% = 97.5% of the normal distribution curve to the left of it.


look for a z-score with .975 to the left of it.


that z-score will be approximately 1.96


since the normal distribution curve is symmetric about the mean, that means the your critical z-score is plus or minus 1.96.


the formula for z-score is z = (x-m)/s


z is the z-score.
x is the raw-score.
m is the raw-mean.
s is the standard deviation.


for your data, to find the high side value of x, you would do:


1.96 = (x-35,000) / 5,000


solve for x to get x = 1.96 * 5,000 + 35,000 = 44,800.


to find the low side value of x, you would do:


-1.96 = (x-35,000) / 5,000


solve for x to get x = -1.96 * 5000 + 35,000 = 25,200.


your minimum starting salary is 25,200.


your maximum starting salary is 44,800.


this is at 95% confidence interval.


this is what it looks like on the normal distribution curve.


<img src = "http://theo.x10hosting.com/2017/060501.jpg" alt="$$$" </>


there are slight differences in my answer and the calculator's answer that are due to rounding.