Question

Given a mean of 7.6 and a standard deviation of 3.1, within how many standard deviations of the mean do the values 10, 9, 11, 5, and 3 fall?

Answer 1

the correct answer is 2

Answer 2

The z-score value of the data is -0.838.

Explanation:

Given : A mean of 7.6 and a standard deviation of 3.1.

To find : How many standard deviations of the mean do the values 10, 9, 11, 5, and 3 fall?

Solution :

Mean
`\mu=7.6`

Standard deviation
`\sigma=3.1`

Values 10, 9, 11, 5, and 3 i.e. x=5

The z-score value for x=5 is given by

`z=(x-\mu)/(\sigma)`

`z=(5-7.6)/(3.1)`

`z=(-2.6)/(3.1)`

`z=-0.838`

The z-score value of the data is -0.838.