Question

a data set has the following characteristics:
mean: 4.9
median: 6
mode: 6
variance: 4

the z-score is the number of standard deviations a data value is away from the mean.

using the formula below, calculate the z-score for the listed data points.

\\z\text{-score: } z_x = \frac{x - \mu}{\sigma}\\

\\(z_1 = \\)
\\(z_5 = \\)
\\(z_{6.5} = \\)

Explanation:

Find the standard deviation

Using the Population Standard Deviation knowledge point

$$
LATEXBLOCK0
$$

Calculate the z-score for x = 1

Using the Z-Score Formula knowledge point

$$ z_1 = \frac{1 - 4.9}{2} = \frac{-3.9}{2} = -1.95 $$

Calculate the z-score for x = 5

Using the Z-Score Formula knowledge point

$$ z_5 = \frac{5 - 4.9}{2} = \frac{0.1}{2} = 0.05 $$

Calculate the z-score for x = 6.5

Using the Z-Score Formula knowledge point

$$ z_{6.5} = \frac{6.5 - 4.9}{2} = \frac{1.6}{2} = 0.8 $$

Answer:

Question 1

\(z_1 =\) <blank>-1.95</blank>

Question 2

\(z_5 =\) <blank>0.05</blank>

Question 3

\(z_{6.5} =\) <blank>0.8</blank>