Question

A population is normally distributed with mean 18 and standard deviation 1.7. (a) Find the intervals representing one, two, and three standard deviations of the mean.

Answer 1

Interval within 1 standard deviation: (16.3,19.7)

Interval within 2 standard deviation: (14.6, 21.4)

Interval within 3 standard deviation: (12.9, 23.1)

Explanation:

We are given the following in the question:

Population mean,
`\mu` = 18

Standard deviation,
`\sigma` = 1.7

We have to find the following intervals:

Interval within 1 standard deviation:

`\mu \pm 1\sigma\\=18 \pm 1.7\\=(16.3, 19.7)`

Interval within 2 standard deviation:

`\mu \pm 2\sigma\\=18 \pm 2(1.7)\\= 18 \pm 3.4\\=(14.6,21.4)`

Interval within 3 standard deviation:

`\mu \pm 3\sigma\\=18 \pm 2(1.7)\\= 18 \pm 5.1\\=(12.9,23.1)`