Question

For a sample of n = 30 scores, X = 45 corresponds to z = 1.50 and X = 40 corresponds to z = +1.00. What are the values for the sample mean and standard deviation?​

Answer 1

Sample mean = 30

Standard deviation = 10

Explanation:

A system with two linear equations can be modeled with the information given in order to find the sample mean (M) and the standard deviation (s):

`z=(X-M)/(s)\\\\1.50=(45-M)/(s) \\1.00=(40-M)/(s)`

Solving the linear system:

`40-M = (45-M)/(1.5)\\M=(15)/(0.5)\\M=30\\\\s=(45-30)/(1.5)\\s=10`

The sample mean is 30 while the standard deviation is 10.