Question 1186922
z = (x - m) / s


z is the z-score
x is the raw score
m is the mean
s is the standard deviation


in your problem:


m = 85.5
s = 4.81
z = -3.41


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


z = (x - m) / s becomes -3.41 = (x - 85.5) / 4.81
multiply both sides of the equation by 4.81 to get:
-3.41 * 4.81 = x - 85.5
add 85.5 to both sides of the equation to get:
-3.41 * 4.81 + 85.5 = x
solve for x to get:
x = 69.0979


that's your raw score.


if the raw score is equivalent to the z-score, you should be able to use a z-score calculator to determine that they both have the same area to the left of them.


i used the z-score calculator at <a href = "https://www.statskingdom.com/normal.html" target = "_blank">https://www.statskingdom.com/normal.html</a> to do that.


for the z-score, i set the mean to 0 and the standard deviation to 1 and then looked for the area to the left of the z-score of -3.41.


these are the results.


<img src = "http://theo.x10hosting.com/2021/103001.jpg" >


for the raw score, i set the mean to 85.5 and the standard deviation to 4.81 and then looked for the area to the left of the raw score of 69.0979


these are the results.


<img src = "http://theo.x10hosting.com/2021/103002.jpg" >


in these displays, you can see that:


p(x <= -3.41) and p(x <= 69.0979) are the same.


the data value you are looking for is the raw score.


your solution is 69.0979.