A distribution of values is normal with a mean of 192.1 and a standard deviation of 95.8. Find P42, which is the score separating the bottom 42% from the top 58%. P42 =

Answer 1

Hello Natalie,

The formula for Z Score is

Z score = ( x – µ ) / σ

Where x is the raw score, µ is the mean and σ is the standard deviation.

with a mean of 192.1 and a standard deviation of 95.8

So we already have the mean and standard deviation

Find P42, which is the score separating the bottom 42% from the top 58%.

(Z < z) = 0.42

Hence, using a Z-Table https://www.ztable.net/ and basic substitution of values, we get:

Z score = ( x – µ ) / σ

-0.202 = (x - 192.1) / 95.8

Simple math this onwards.

Hope this helps,

Samantha

Answer 2

First find z-score such that (Z < z) = 0.42, which is approximately -0.202

Then use formula for standardized z score, where x = score

z = (x - mean)/standard deviation

-0.202 = (x - 192.1)/95.8 and solve for x.

x = 172.75