The population 3, 4, 9, 14, and 20 has a mean of 10 and a standard deviation of 6.356. The z-scores for each of the five data values are z3 ≈ −1.101, z4 ≈ −0.944, z9 ≈ −0.157, z14 ≈ 0.629, and z20 ≈ 1.573. Find the mean and the standard deviation of these z-scores.

First, we find the square of the difference of the z values provided and sum them up giving us a value of 4.997956. We, therefore, calculate the sum of the sample mean given the number of samples to be 5 which gives us zero(0).

To calculate the standard deviation we use the formula that takes the square root of the inverse of the number of samples (n)*(the summation of the square of the difference between the sample and the mean which gives us 1.

*Step-by-step explaination

Given z3= -1.101, (z3 minus mean of z3)^2= 1.212201

Given z4= -0.944, (z4 minus mean of z4)^2=0.891136

Given z9= -0.157, (z9 minus mean of z9)^2= 0.024649

Given z14= 0.629, (z14 minus mean of z14)^2= 0.395641

Given z20= 1.573, (z20 minus mean of z20)^2= 2.474329

Therefore the summation of all Z values = Zero(0)

Also, the summation of (z values minus the mean of z values)^2= 4.997956

Therefore where n =5,

The sample mean of z values is given by the summation of z values divided by n = Zero (0)

To calculate standard deviation we use the formula that takes the square root of the inverse of the number of samples (n)*(the summation of the square of the difference between the sample and the mean which gives us 1.