Question 1203818
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 <a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>


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.


<img src = "http://theo.x10hosting.com/2023/092201.jpg">