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 x lies above or below the mean and by how many standard deviations.
a. z = 2 (simplify your answer.)
b. z = \\( \square \\) (simplify your answer.)

Explanation:

Step1: Recall the formula for z - score

The formula for the z - score when dealing with a population is \(z=\frac{x-\mu}{\sigma}\).

Step2: Substitute the values for part b

Given \(x = 88\), \(\mu=87\), and \(\sigma = 2\).
Substitute these values into the formula: \(z=\frac{88 - 87}{2}\)

Step3: Simplify the expression

\(z=\frac{1}{2}=0.5\)

Answer:

\(0.5\)