The z-score formula is given by:

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

where:

• $x$ is the value for which we are calculating the z-score (30.2),
• $\mu$ is the sample mean (33.7),
• $\sigma$ is the sample standard deviation (7.2).

Substitute the values into the formula:

$z = \frac{30.2 - 33.7}{7.2} = \frac{-3.5}{7.2} \approx -0.49$

So, the z-score is approximately $-0.49$.

Would you like more details, or have any questions?

Here are five related questions to expand your understanding:

1. What does a negative z-score represent in a dataset?
2. How do you interpret z-scores in the context of a normal distribution?
3. Can you calculate the probability of obtaining a value less than 30.2 using the z-score?
4. How do you calculate the z-score for a population instead of a sample?
5. How would the z-score change if the standard deviation were smaller?

Tip: A z-score tells you how many standard deviations a value is from the mean.