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

Question

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

Julianne Mccoy · Accepted Answer

The sample size is 5. It is appropriate to find t score.
z score shall be calculated only when the sample size is

\geq 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 - μ}{S E} = \frac{60 - 60}{1.5} = \frac{0}{1.5} = 0

Note: If the Value of X is equal to Mean i.e.,

μ

the z score is always 0.

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

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