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Part 1
For a sample of 225 female​ heights, the mean was 65.8 inches and the standard deviation was 2.8 inches. The shortest person in this sample had a height of 59 inches.
a. Find the​ z-score for the height of 59 inches.
Find the​ z-score.
zequals

enter your response here ​(Round to one decimal place as​ needed.)

To find the z-score for the height of 59 inches, we use the z-score formula:

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

where:
- \( X \) is the value (59 inches),
- \( \mu \) is the mean (65.8 inches),
- \( \sigma \) is the standard deviation (2.8 inches).

Substitute the values into the formula:

\[
z = \frac{59 - 65.8}{2.8}
\]

Calculate:

\[
z = \frac{-6.8}{2.8} \approx -2.43
\]

Rounded to one decimal place, the z-score is:

\[
z \approx -2.4
\]

Would you like more details or have any questions? Here are some related questions:

1. What is the significance of a z-score?
2. How does the z-score relate to the standard normal distribution?
3. What does a negative z-score indicate about a data point?
4. How would you interpret a z-score of 0?
5. What is the probability associated with a z-score of -2.4?
6. How would the z-score change if the height was 70 inches instead of 59 inches?
7. What is the range of z-scores for typical values in a normal distribution?
8. Can z-scores be used to compare different datasets?

**Tip:** When calculating z-scores, always round to the required number of decimal places for consistency.

Learn how to calculate the z-score for a height of 59 inches from a sample with mean 65.8 inches and standard deviation 2.8 inches. Understand the significance of z-scores in statistics. Suitable for high school students studying statistics.

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