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

a) -0.75

b) -1.5

c) -3

Step-by-step explanation:

The question asks to convert a given value to z score with different sample sizes.

We are given:

Population Mean = u = 40

and

Standard deviation = s = 8

The task is to convert 34 to z-score using 3 different sample sizes.

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

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

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

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

From here we can see that increasing the sample sizes increases the magnitude of z-score.

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.