A distribution of values is normal with a mean of 42.3 and a standard deviation of 49.1. Find P42, which is the score separating the bottom 42% from the top 58%.

Question

This has me 100% lost. I am not sure where to even start.

Answer 1

First find the z-score that corresponds to a probability of 0.42. From the standard normal probabilities table hat would be approximately z = -0.2.

Use the following equation to find x = score corresponding to 42nd percentile:

z = (x - mean)/SD

where z = -0.2, mean = 42.3 and SD = 49.1

-0.2 = (x - 42.3)/49.1

x = -0.2 * 49.1 + 42.3 = 32.48