00:01
For this question, we are asked which of the following statements is not true concerning the attributes of z scores.
00:08
A states that z scores are positive for data values above the mean of the distribution.
00:14
Let's first look at how z scores are constructed.
00:18
It's the value of a random variable minus the mean of its distribution, divided by the standard deviation of the distribution.
00:28
You can see here that if x is bigger than the mean, then this quantity is going to be positive.
00:36
So z scores are indeed positive for data values above the mean of the distribution.
00:42
So a is correct.
00:44
B says z scores are negative for data values below the mean of the distribution.
00:49
Seeing the exact same reasoning, this is below the mean, or smaller than the mean, then the z score is going to come out negative.
01:01
So b is also correct.
01:04
D says z scores indicate how many standard deviations and observable, then the z scores indicate how many is away from the mean...