Question

If a set of data are normally distributed with at least 68% of scores falling between scores 16.5 and 19.5. If these values mark the first standard deviation from the mean, then what are the values of the mean and standard deviation in this normal distribution?

Answer 1

Answer:
`\mu=18` and
`\sigma= 1.5`

Explanation:

Let
`\mu` = mean and
`\sigma` = standard deviation.

Given : If a set of data are normally distributed with at least 68% of scores falling between scores 16.5 and 19.5.

If these values mark the first standard deviation from the mean, then

`\mu -\sigma=16.5----(1)\\\mu +\sigma=19.5-----(2)`

Adding (1) and (2) ,we get

`2\mu=36\\\Rightarrow\ \mu=18`

Subtract (1) from (2) , we get

`2\sigma= 3\\\Rightarrow\ \sigma= 1.5`

Hence, the values of the mean and standard deviation in this normal distribution are :

`\mu=18` and
`\sigma= 1.5`