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.