SOLUTION: The scores on the entrance exam at a well-known, exclusive law school are normally distributed with a mean score of 125 and a standard deviation equal to 46. At what value should t

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Question 993924: The scores on the entrance exam at a well-known, exclusive law school are normally distributed with a mean score of 125 and a standard deviation equal to 46. At what value should the lowest passing score be set if the school wishes only 2.5 percent of those taking the test to pass?
Set lowest passing score to
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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.