Question

The mean for a data set is 60. The Z-score for

data point a is 0. The z-score for data point b
is -0.4. Which are the possible values for data
point a and b?
A. a = 0 and b = 61.2
B. a = 0 and b = 58.8
C. a = 60 and b = 61.2
D. a = 60 and b = 58.8

Answer 1

D. a = 60 and b = 58.8

Explanation:

Z-score:

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Z-score for data point a is 0.

This means that a is the mean, that is, a = 60.

The z-score for data point b is -0.4.

This means that b must be a value below the mean, that is, a value below 60.

The option that satisfies a = 60 and b < 60 is option D, which is the answer.