Question

What is the z-score of X, if n = 4, `mu= 60`, SD =3, and X =60?

Answer 1

`z=0`

Explanation:

I have my own doubt about the correctness of the problem.

The sample size is `5`. It is appropriate to find `t` score.

`z` score shall be calculated only when the sample size is `>=30`
Some statisticians, if they believe the population distribution is normal, use `z` score even if the sample size is less than 30.

You didn't state explicitly for which distribution you want to compute `z`. It may be an observed distribution or it may be a sampling distribution.

Since you have asked the question, I shall answer by assuming it is a sampling distribution.

`SE = (SD)/sqrtn=3/sqrt4=3/2=1.5`

`z=(x-mu)/(SE)=(60-60)/1.5=0/1.5=0`

Note: If the Value of `X` is equal to Mean i.e., `mu` the `z` score is always 0.