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

Answer:

Sample mean = 30

Standard deviation = 10

Step-by-step 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):

$z=\frac{X-M}{s}\\\\1.50=\frac{45-M}{s} \\1.00=\frac{40-M}{s}$

Solving the linear system:

$40-M = \frac{45-M}{1.5}\\M=\frac{15}{0.5}\\M=30\\\\s=\frac{45-30}{1.5}\\s=10$

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