SOLUTION: A distribution of values is normal with a mean of 144 and a standard deviation of 73.2. Find P4, which is the score separating the bottom 4% from the top 96%.

Algebra ->  Probability-and-statistics -> SOLUTION: A distribution of values is normal with a mean of 144 and a standard deviation of 73.2. Find P4, which is the score separating the bottom 4% from the top 96%.      Log On


   

Question 1203818: A distribution of values is normal with a mean of 144 and a standard deviation of 73.2.
Find P4, which is the score separating the bottom 4% from the top 96%.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
mean is 144.
standard deviation is 73.2
P4 is the score that separates the bottom 4% from the top 96%.

use a normal distribution calculator to find the z-score that has 4% of the area under the normal distribution curv to the left of it.

one such calcuator can be found at https://davidmlane.com/hyperstat/z_table.html

this calculator tells you that the the z-score with an area to the left of it of .04 is equal to -1.751.

use the z-score formula to find the associated raw score.

the z-score formula is z = (x - m) / s
x is the z-score
x is the raw score
m is the mean
s is the standard deviation

the formula becomes -1.751 = (x - 144) / 73.2
solve for to get:
z = -1.751 * 73.2 + 144 = 15.8268.

P4 is equal to 15.8268.
that's the score that separates the bottom 4% from the top 96% of the scores when the mean is 144 and the standard deviation is 73.2.

here's what the calculator results look like.