Question

A test is normally distributed with a mean of 40 and a standard deviation of 7. (a) what score would be needed to be in the 87th percentile? (b) what score would be needed to be in the 28th percentile?

Answer 1

We have given Mean = 40 and standard deviation = 7

a) Here we have asked to find the 87th percentile.

We know that -

87th percentile (X) = Z_0.87 * +

From Z table we get Z_0.87 = 1.1264

Hence we get X = (1.1264 * 7) + 40

87th percentile X = 47.88

87th Percentile = 47.88 (Rounded to two decimal places)

b)

28th percentile (X) = Z_0.28 * +

From Z table we get Z_0.28 = -0.5828

Hence we get X = (-0.5828 * 7) + 40

28th percentile X = 35.92

28th Percentile = 35.92 (Rounded to two decimal places)

Hope this will help you.Thank you :)