Question

For a population with $\mu=40$ and $\sigma=8$ a. Find the z-score for each of the following $X$ values. (Note: You should be able to find these values using the definition of a $z$ -score. You should not need to use a formula or do any serious calculations. $$\begin{array}{lll}X=44 & X=48 & X=56 \\X=38 & X=34 & X=32\end{array}$$ b. Find the score ( $X$ value) that corresponds to each of the following z-scores. (Again, you should not need a formula or any serious calculations. $$\begin{array}{lll}z=1.00 & z=0.25 & z=1.50 \\z=-0.50 & z=-1.25 & z=-2.50\end{array}$$

Name: Problem 4, Chapter 5: Essentials of Statistics for the Behavioral Sciences
Uploaded: 2023-09-24T13:35:19-08:00
Channel: Donna Densmore

   For a population with $\mu=40$ and $\sigma=8$
a. Find the z-score for each of the following $X$ values. (Note: You should be able to find these values using the definition of a $z$ -score. You should not need to use a formula or do any serious calculations.
$$\begin{array}{lll}X=44 & X=48 & X=56 \\X=38 & X=34 & X=32\end{array}$$
b. Find the score ( $X$ value) that corresponds to each of the following z-scores. (Again, you should not need a formula or any serious calculations.
$$\begin{array}{lll}z=1.00 & z=0.25 & z=1.50 \\z=-0.50 & z=-1.25 & z=-2.50\end{array}$$

Essentials of Statistics for the Behavioral Sciences

Frederick J.… 9th Edition

Chapter 5, Problem 4

Instant Answer

Solved by Expert Donna Densmore

09/24/2023

Step 1

We are asked to find the z-score for each of the given $X$ values. The z-score is calculated as $z=\frac{X-\mu}{\sigma}$. Show more…

Show all steps

Thanks for your feedback!

For a population with $\mu=40$ and $\sigma=8$ a. Find the z-score for each of the following $X$ values. (Note: You should be able to find these values using the definition of a $z$ -score. You should not need to use a formula or do any serious calculations. $$\begin{array}{lll}X=44 & X=48 & X=56 \\X=38 & X=34 & X=32\end{array}$$ b. Find the score ( $X$ value) that corresponds to each of the following z-scores. (Again, you should not need a formula or any serious calculations. $$\begin{array}{lll}z=1.00 & z=0.25 & z=1.50 \\z=-0.50 & z=-1.25 & z=-2.50\end{array}$$

Play audio

Feedback

Donna Densmore and 61 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Z-Score

A z?score indicates how many standard deviations a single data point is from the mean. It is calculated by taking the difference between a raw score and the mean of the distribution and then dividing by the standard deviation. This concept is fundamental for understanding how individual scores relate to the overall distribution.

Standardization

Standardization is the method of converting raw data into z-scores, which places different scores on a common scale. By standardizing data, comparisons can be made across different distributions or populations, regardless of their original units or scales.

Normal Distribution

The normal distribution is a symmetric, bell-shaped distribution that is frequently used in statistics. Many analyses assume that data follow a normal distribution, and the properties of z-scores are especially useful in this context for calculating probabilities and percentiles.

Please give Ace some feedback