Question

for a sample with a standard deviation of $s = 15$, describe the location of each of the following $z$-scores in terms of its position relative to the mean. for example, $z= + 1.00$ is a location that is 15 points above the mean.
a. $z=-1.20$
b. $z = + 0.80$
c. $z=+2.00$

Explanation:

Step1: Recall z - score formula meaning

The z - score formula is $z=\frac{x - \mu}{s}$, where $x$ is the data point, $\mu$ is the mean and $s$ is the standard deviation. A z - score tells us how many standard - deviations a data point is from the mean.

Step2: Calculate position for $z=-1.20$

Since $s = 15$, the position relative to the mean is $z\times s=-1.20\times15=-18$. So it is 18 points below the mean.

Step3: Calculate position for $z = + 0.80$

The position relative to the mean is $z\times s=0.80\times15 = 12$. So it is 12 points above the mean.

Step4: Calculate position for $z = + 2.00$

The position relative to the mean is $z\times s=2.00\times15=30$. So it is 30 points above the mean.

Answer:

a. 18 points below the mean
b. 12 points above the mean
c. 30 points above the mean