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

Solution:

Population with a mean of 40 = u

The Standard deviation of 8 = s

So now, we are given a value to convert it into a 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)

It is given that, 

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

Then, z -score = (34 - 40)/(8/√1)

z - score = -0.75

b) M = 34 for a sample of n = 4

Then, z -score = (34 - 40)/(8/√4)

z - score = -1.5

c) M = 34 for a sample of n = 16

Then, z -score = (34 - 40) / (8/√16)

z - score = -3

Therefore, for a population with a mean of 40 and a standard deviation of 8 and the z-score corresponding to each of the following samples are,

X = 34 for a sample of n = 1 score, z- score = -0.75

M = 34 for a sample of n = 4, z- score = -1.5

M = 34 for a sample of n = 16, z- score = -3

---

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.

Summary:

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

X = 34 for a sample of n = 1 score, z- score = -0.75 , M = 34 for a sample of n = 4, z- score = -1.5, M = 34 for a sample of n = 16, z- score = -3