To calculate the z score, we use the formula:

$z = \frac{x - \mu}{\sigma}$

Where:

• $z$ = z-score
• $x$ = raw score (2670 in this case)
• $\mu$ = mean (3540 calories)
• $\sigma$ = standard deviation (325 calories)

Now, substitute the values:

$z = \frac{2670 - 3540}{325} = \frac{-870}{325} \approx -2.68$

The z score corresponding to 2670 calories is approximately -2.68.

Would you like further details or have any questions?

Here are 5 related questions for deeper exploration:

1. What does a z score of -2.68 imply about the 2670-calorie intake?
2. How do you interpret z scores in terms of normal distribution?
3. What percentage of the population consumes fewer than 2670 calories per day based on this data?
4. How do we calculate the probability from a z score using standard normal distribution tables?
5. If the calorie intake were 4000 calories, what would be the z score?

Tip: The z score tells you how many standard deviations a particular value is from the mean. Negative z scores indicate values below the mean, while positive ones indicate values above it.