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

Nov 12, 2015

$z = 0$

#### 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 $\ge 30$
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.

$S E = \frac{S D}{\sqrt{n}} = \frac{3}{\sqrt{4}} = \frac{3}{2} = 1.5$

$z = \frac{x - \mu}{S E} = \frac{60 - 60}{1.5} = \frac{0}{1.5} = 0$

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