Question

A set of data has a normal distribution with a mean of 50 and a standard deviation of 8. What percent of the data should fall between 42 and 58?

Answer 1

Let's calculate the z scores for 42 and 58:

        42 - 50
z = ------------- = -1
             8
          58-50
z = --------------- = 1
             8

so the question becomes:  what percent of the data should fall within 1 std. dev. of the mean?  Referring to the empirical formula:  68%   (answer)

Answer 2

Answer with explanation:

Mean$\mu$ = 50

Standard Deviation$\sigma$ =8

$\mu-\sigma=50-8=42$

$\mu+\sigma=50+8=58$

$\mu-\sigma <50<\mu+\sigma\\\\50-8 <50<50+8\\\\42<50<58$

⇒When you will read the normal distribution curve, you will find that, about 68% of the data falls between 1 standard deviation right and 1 standard deviation left of the mean.

→68% of the data falls between 42 and 58.