Question

A population has mean u=25 and standard deviation o=6. Round the answers to two decimal places as needed.
A) Find the z-score for a population value of 4.

Answer 1

find the z-score for a population of 28

Answer 2

c) What number has a -score of 2.8?

Answer 3

To find the z-score for a given population value, you can use the formula:

\[
z = \frac{X - \mu}{\sigma}
\]

where:
- \(X\) is the value for which you want to find the z-score,
- \(\mu\) is the population mean,
- \(\sigma\) is the standard deviation.

In this case:
- \(X = 4\)
- \(\mu = 25\)
- \(\sigma = 6\)

Substituting these values into the formula:

\[
z = \frac{4 - 25}{6} = \frac{-21}{6} = -3.5
\]

Thus, the z-score for a population value of 4 is \(\boxed{-3.50}\).

Answer 4

To find the z-score for the population value of 28, we will use the same formula:

\[
z = \frac{X - \mu}{\sigma}
\]

Where:
- \(X = 28\)
- \(\mu = 25\) (the population mean)
- \(\sigma = 6\) (the standard deviation)

Substituting these values into the formula:

\[
z = \frac{28 - 25}{6} = \frac{3}{6} = 0.5
\]

Thus, the z-score for a population value of 28 is \(\boxed{0.50}\).

Answer 5

To find the number that has a z-score of 2.8, we can rearrange the z-score formula:

\[
z = \frac{X - \mu}{\sigma}
\]

We can solve for \(X\):

\[
X = z \cdot \sigma + \mu
\]

Given:
- \(z = 2.8\)
- \(\mu = 25\) (the population mean)
- \(\sigma = 6\) (the standard deviation)

Substituting these values into the formula:

\[
X = 2.8 \cdot 6 + 25
\]

Calculating the value:

\[
X = 16.8 + 25 = 41.8
\]

Thus, the number that has a z-score of 2.8 is \(\boxed{41.80}\).