Question

compute the z - score corresponding to each of the values of x below.
a. ( x = 28 ), ( s = 4 ), ( overline{x}=20 ) b. ( x = 88 ), ( mu = 87 ), ( sigma = 2 ) c. ( mu = 45 ), ( sigma = 5 ), ( x = 45 )
d. ( s = 6 ), ( x = 35 ), ( overline{x}=50 ) e. in parts a - d, state whether the z - score locates x within a sample or a population. f. in parts a - d, state whether each value of lies above or below the mean and by how many standard deviations.
a. ( z=square ) (simplify your answer.)

Explanation:

Step1: Recall the formula for z - score for sample

The formula for the z - score of a sample is \(z=\frac{x-\bar{x}}{s}\), where \(x\) is the data point, \(\bar{x}\) is the sample mean, and \(s\) is the sample standard deviation.

Step2: Substitute the values into the formula

Given \(x = 28\), \(\bar{x}=20\), and \(s = 4\).
Substitute these values into the formula: \(z=\frac{28 - 20}{4}\).

Step3: Simplify the expression

First, calculate the numerator: \(28-20 = 8\). Then, divide by the denominator: \(\frac{8}{4}=2\).

Answer:

\(2\)