SOLUTION: A normal distribution has a standard deviation equal to 10. What is the mean of this normal distribution if the probability of scoring below x=10 is .5000?

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Question 1185987: A normal distribution has a standard deviation equal to 10. What is the mean of this normal distribution if the probability of scoring below x=10 is .5000?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
standard deviation is equal to 10.
probability of scoring below x = 10 is .5.

the mean of a normal distribution has an area to the left of it and an area to the right of it equal to .5.

that means the mean is right in the middle of the normal distribution.

if the probability of scoring below x = 10 is .5, then x = 10 must be the mean of the normal distribution.

if you want to go through the math, it will go like this.

the z-score formula is:

z = (x - m) / s

the area to the left of a z-score of 0 is equal to .5.
x = 10
s = 10

0 = (10 - m) / 10
multiply both sides of the equation by 10 to get:
10 * 0 = 10 - m
simplify to get:
0 = 10 - m
add m to both sides of the equation to get:
m = 10.