Question

complete the statement \z = \ for each data value.
a. a data value 0.2 standard deviation below the mean.
b. a data value 1.8 standard deviations below the mean.
c. a data value 1.4 standard deviations above the mean.

a. z = \square
(type an integer or a decimal.)

Explanation:

Step1: Recall the formula for z - score

The z - score formula is \(z=\frac{x - \mu}{\sigma}\), where \(x\) is the data value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation. If a data value is \(k\) standard deviations below the mean, then \(z=-k\); if it is \(k\) standard deviations above the mean, then \(z = k\).

Step2: Calculate z - score for part (a)

Since the data value is \(0.2\) standard deviation below the mean, using the rule from Step 1, \(z=- 0.2\).

Step3: Calculate z - score for part (b)

Since the data value is \(1.8\) standard deviations below the mean, using the rule from Step 1, \(z=-1.8\).

Step4: Calculate z - score for part (c)

Since the data value is \(1.4\) standard deviations above the mean, using the rule from Step 1, \(z = 1.4\).

Answer:

a. \(z=-0.2\)
b. \(z=-1.8\)
c. \(z = 1.4\)