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 = 0 ) (simplify your answer.)
d. ( z=-2.5 ) (simplify your answer.)
e. for part a, determine whether the z - score locates x within a sample or a population. choose the correct answer below.
the z - score locates x within a sample.
for part b, determine whether the z - score locates x within a sample or a population. choose the correct answer below.
the z - score locates x within a

Explanation:

Step1: Recall the formula for z - score

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

Step2: Analyze part (b)

In part (b), we have \(x = 88\), \(\mu=87\), \(\sigma = 2\). Since we are using \(\mu\) (population mean) and \(\sigma\) (population standard deviation), the formula \(z=\frac{x-\mu}{\sigma}\) is used.

Answer:

The z - score locates \(x\) within a population.