Question

A distribution of values is normal with a mean of 160 and a standard deviation of 4.

Find the interval containing the middle-most 30% of scores:

Enter your answer using interval notation. Example: [2.1,5.6)
Your numbers should be accurate to 1 decimal places.
Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Solution:

Given that,

Middle 30% as the to z values are -0.385 and 0.385

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = -0.385 * 4 + 160 = 158.5

and

x = 0.385 * 4 + 160 = 161.5

Answer = 158.5 and 161.5