Question

An educational study to be conducted requires a test score in the middle 40% range. If mean= 100 and standard deviation= 15. find the highest and lowest acceptable test scores that would enable a candidate to participate in the study. Assume the variable is normally distributed.

- I need help finding it with the standard normal distribution table with z score only. Thank you!

Answer 1

Mean = = 100

SD = = 15

Middle 40% range corresponds to area = 0.40/2 = 0.20 on either side of mid value.

Table of Area Under Standard Normal Curve gives Z = 0.525

Low side:

Z = - 0.525 = (X - 100)/15

So,

X = 100 - (0.525 X 15) = 100 - 7.875 = 92.125

High side:

Z = 0.525 = (X - 100)/15

So,

X = 100 + (0.525 X 15) = 100 + 7.875 = 107.875

So,

Highest acceptable test score = 107.875

Lowest acceptable test score = 92.125