Consider a set of data in which the sample mean is 33.7
and the sample standard deviation is 7.2
.  Calculate the z-score given that x=30.2
.  Round your answer to two decimal places.

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.

Consider a set of data in which the sample mean is 33.7 and the sample standard deviation is 7.2. Calculate the z-score given that x=30.2. Round your answer to two decimal places.

Learn how to calculate the z-score for x = 30.2, given a sample mean of 33.7 and a sample standard deviation of 7.2. This problem involves understanding key statistical concepts such as the z-score formula, mean, and standard deviation. Suitable for high school students in Grades 10-12.

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