Question

Solve the problem. A variable x has the possible observations shown below. Possible observations of x: -3 -1 0 1 1 2 4 4 5 Find the z-score corresponding to an observed value of x of 2.

Answer 1

The z-score corresponding to an observed value of x of 2 is 0.215.

Explanation:

We are given that a variable x has the possible observations shown below;

Possible observations of X: -3, -1, 0, 1, 1, 2, 4, 4, 5.

Firstly, we will find the mean and the standard deviation of X, i.e;

Mean of X, (
`\mu`) =
`(\sum X)/(n)`

=
`((-3)+ (-1)+ 0+ 1+ 1+ 2+ 4+ 4+ 5)/(9)`

=
`(13)/(9)` = 1.44

Standard deviation of X, (
`\sigma`) =
`\sqrt{(\sum (X-\bar X)^(2) )/(n-1) }`

=
`\sqrt{((-3-1.44)^(2)+(-1-1.44)^(2)+......+(4-1.44)^(2)+(5-1.44)^(2) )/(9-1) }`

= 2.603

Now, the z-score corresponding to an observed value of x of 2 is given by;

z-score =
`(X-\mu)/(\sigma)`

=
`(2-1.44)/(2.603)` = 0.215.