For a sample of n = 100 scores,X = 45 corresponds to z = 0.50 and X = 52 corresponds to z = +1.00.What are the values for the sample mean and standard deviation?
A)M = 31 and s = 7
B)M = 31 and s = 14
C)M = 38 and s = 7
D)M = 38 and s = 14

Question

Quizplus · Accepted Answer

The sample mean (M) can be found by using the z-score formula for both given values and solving for M. The formula is $z = \frac{(X - M)}{s}$, where X is the score, M is the mean, and s is the standard deviation. For X = 45 and z = 0.50, and for X = 52 and z = 1.00, solving these equations simultaneously gives M = 38 and s = 14.

For a Sample of N = 100 Scores,X = 45