Question

A normal distribution has a mean of 36 and a standard deviation of 5. Find the range of values that represent the middle68% of the distribution.

Answer 1

Given:

The mean of the normal distribution is 36.

$\mu=36$

The standard deviation is 5.

$\sigma=5$

The distribution percent is 68 %.

Required:

We need to find the range of the values that represent the middle 68% of the distribution.

Explanation:

Recall that 68% of the data is within 1 standard deviation (σ) of the mean (μ),

Consider the range formula for within 1 standard deviation (σ) of the mean (μ),

$Range=(\mu-\sigma,\mu+\sigma)$$Substitute\text{ }\mu=36,\text{ and }\sigma=5\text{ in the formula.}$

$Range=(36-5,36+5)$$Range=(31,41)$

Final answer:

$Range=(31,41)$