What raw score is at the 34th percentile (34.13 to be exact) when the mean of the distribution is 50 and the standard deviation is 4?

Let x = the raw score at the 34th percentile.

Given:

μ = 50, the mean

σ = 4, the standard deviation

The z-score is

z = (x - μ) / σ = (x - 50/4

From the normal tables, obtain z = - 0.41 for 34% of the area.

Therefore

(x - 50) / 4 = - 0.41

x - 50 = - 1.64

x = 48.36

Answer: 48.36