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 = 0.5 ) (simplify your answer.)
c. ( 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 into the formula

Given \(\mu = 45\), \(\sigma=5\), and \(x = 45\). Then \(z=\frac{45 - 45}{5}\).

Step3: Simplify the expression

\(\frac{45 - 45}{5}=\frac{0}{5}=0\)

Answer:

\(0\)