Question

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?

Answer 1

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