Statistics.. FInding what X is supposed to be in order to find the Z score?

Question

Math SAT scores or all math majors in a school are normally distributed with a mean of 627 and a standard diviation of 60.5 at (x-n)627,60.5 if the school board wants to identify the top 5.5% of the students on the test what score should be used as a cut off

Answer 1

Hi, Amber.

1. Draw bell curve and label "x" and "z" corresponding scales.
2. Shade in area under the curve that you are seeking.
3. Use Z-Score chart to look up area to the left of the line of demarcation (line in the sand called the Z-score) to determine the Z-score.
4. Convert that Z-score to an x value.

mew is population mean of 627

lower case sigma is population standard deviation 60.5

x = mew + z times standard deviation

Another way to say it is z = (x minus mew) and this difference is divided by the standard deviation.

In your case, you want the Z score separating the top 5.5% from the bottom 94.5%. From the Z-Score chart, that is a Z-Score of +1.6

So, to convert that to "x" simply plug in x = 627 + (+1.6)*60.5 = 723.8

So, answer x=723.8 score separates top 5.5% from bottom 94.5%.

Amber, I am not sure if you received the video I did for you, but I would like to help you better understand this course. please contact me for my tutoring services. Thank you.

Ira S.