**Daily Caloric Intake According to one source, people eat on average 3540calories per day. If the standard deviation is 325calories, find the *z* score for each raw score. Round *z* scores to at least two decimal places.**

The *z* score corresponding to 3320 calories is

To find the **z-score** corresponding to a raw score, we use the z-score formula:

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

Where:
- \( X \) = raw score (3320 calories)
- \( \mu \) = mean (3540 calories)
- \( \sigma \) = standard deviation (325 calories)

Now substitute the values:

\[
z = \frac{3320 - 3540}{325}
\]

\[
z = \frac{-220}{325} = -0.6769
\]

Rounding to two decimal places:

\[
z = -0.68
\]

Thus, the **z-score** corresponding to 3320 calories is **-0.68**.

Would you like further details or have any questions?

Here are five related questions:
1. What is the interpretation of a negative z-score?
2. How would the z-score change if the raw score were higher than the mean?
3. What is the probability associated with this z-score?
4. How do you compute the z-score for a raw score of 3800 calories?
5. How does the standard deviation affect the spread of z-scores?

**Tip:** The z-score tells you how many standard deviations a raw score is from the mean.

Daily Caloric Intake According to one source, people eat on average 3540 calories per day. If the standard deviation is 325 calories, find the z-score for each raw score. Round z scores to at least two decimal places. The z score corresponding to 3320 calories is

Learn how to calculate the z-score for a raw score of 3320 calories, given a mean of 3540 calories and a standard deviation of 325 calories. This problem covers statistical concepts such as z-scores and standard deviation, and is suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation