https://file.aiquickdraw.com/mathbot/file/1729485006207utb8pcwz.jpg

The problem in the image asks for the percentage of bone density scores that are considered "significantly high," meaning at least 2 standard deviations above the mean. 

For a normally distributed set of scores:

- The mean (µ) is 0, and the standard deviation (σ) is 1.
- Scores that are "significantly high" are those at least 2 standard deviations above the mean, i.e., \( z \geq 2 \).

### Using the Empirical Rule (68-95-99.7 Rule):
- About 95% of the data falls within 2 standard deviations (between \( z = -2 \) and \( z = 2 \)).
- Therefore, 5% of the data lies outside this range.
- Since the distribution is symmetric, half of this 5% (i.e., 2.5%) corresponds to scores that are **significantly high** (greater than 2 standard deviations above the mean).

### Answer:
The percentage of bone density scores that are significantly high is **2.5%**.

Would you like a more detailed explanation or have any questions?

---

Here are five related questions to extend your understanding:
1. What percentage of scores are considered significantly low (below \( z = -2 \))?
2. How would the percentage change if we were looking for scores more than 3 standard deviations above the mean?
3. What percentage of scores are within 1 standard deviation from the mean?
4. How does the shape of the normal distribution help us determine these percentages?
5. How do standard deviations relate to z-scores in a normal distribution?

**Tip:** The Empirical Rule is useful for quickly estimating the spread of data in a normal distribution without needing to calculate exact probabilities.

For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that are significantly high (at least 2 standard deviations above the mean).

Learn how to calculate the percentage of bone density scores that are significantly high, which means at least 2 standard deviations above the mean, using the Empirical Rule for normal distribution. This problem covers statistical concepts like standard deviation and z-scores, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation