The height of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachael is at the 99th percentile in height for adult woman, then her height, in inches, is about what

To determine Rachael's height at the 99th percentile for adult women, we can use the properties of the normal distribution.

### Key details:
- Mean height (\(\mu\)) = 65 inches
- Standard deviation (\(\sigma\)) = 2 inches
- Percentile = 99th percentile

To find Rachael's height, we need to use the **z-score** corresponding to the 99th percentile in a standard normal distribution. This z-score is approximately 2.33 (from z-tables or standard normal distribution calculators).

The formula for finding the height from the z-score is:

\[
\text{Height} = \mu + z \cdot \sigma
\]

Substitute the values:

\[
\text{Height} = 65 + 2.33 \cdot 2 = 65 + 4.66 = 69.66 \, \text{inches}
\]

### Conclusion:
Rachael's height is approximately **69.66 inches**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the z-score for the 95th percentile?
2. How would the height change if the standard deviation was larger?
3. What percentage of women are taller than 67 inches?
4. How would you calculate the probability that a randomly selected woman is shorter than 63 inches?
5. What is the 50th percentile height for adult women?

**Tip:** Z-scores help convert data points into standard deviations from the mean, which is crucial for interpreting percentiles in normally distributed data.

The height of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachael is at the 99th percentile in height for adult woman, then her height, in inches, is about what?

Learn how to calculate the height of a woman at the 99th percentile, given that the heights of adult women follow a normal distribution with a mean of 65 inches and a standard deviation of 2 inches. Using z-scores and the properties of normal distribution, this problem is ideal for students in Grades 9-12.

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