Question 993924
you want a critical z-factor such that less than 2.5% will pass.


look up in the z-score table for a z-score that has an area to the left of it of (1 - .025) = .975


that z-factor will be your critical z-factor and the value will be 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 mean
s is the standard deviation


since you know z and m and s, you can solve for x.


formula becomes:


1.96 = (x - 125) / 46


solve for x to get x = 215.16


that's the score they need to pass.


here's a picture of what that looks like.


the first picture is the z-factor.
the second picture is the raw score.


the area of the normal distribution curve that is covered is shown in the picture and in digits at the bottom.


<img src = "http://theo.x10hosting.com/2015/100301.jpg" alt="$$$" </>


<img src = "http://theo.x10hosting.com/2015/100302.jpg" alt="$$$" </>