Question

For a population with a mean of 40 and a standard deviation of 8 find the z-score corresponding to each of the following samples.

X = 34 for a sample of n = 1 score:

M = 34 for a sample of n = 4

M = 34 for a sample of n = 16

Answer 1

(a) -0.75

(b) -1.5

(c) -3

Explanation:

The formula for calculating z-score is :

`Z= \frac{\bar{x}-\mu}{(\sigma)/(√(n)) }`

(a) [/tex]\bar{x} [/tex] = 34

μ = 40

n = 1

σ = 8

Putting all values,

Z = \frac{34-40}{\frac{8}{\sqrt{1}} }

⇒ Z= -0.75

(b) Z = \frac{34-40}{\frac{8}{\sqrt{4}} }

⇒ Z= -1.5

(c) Z = \frac{34-40}{\frac{8}{\sqrt{16}} }

⇒ Z= -3

Answer 2

a) -0.75

b) -1.5

c) -3

Explanation:

Population Mean = u = 40

Standard deviation = s = 8

We are given a value to convert it into z-score with different sample sizes.

For a given sample size "n", the formula to calculate the z-score is:

`z=(x-u)/((s)/(√(n) ) )`

For x = 34 and n=1, we get:

`z-score=(34-40)/((8)/(√(1) ) ) = -0.75`

For x = 34 and n = 4, we get:

`z-score=(34-40)/((8)/(√(4) ) ) = -1.5`

For x = 34 and n = 16, we get:

`z-score=(34-40)/((8)/(√(16) ) ) = -3`