https://file.aiquickdraw.com/mathbot/file/17263129162454p865mw1.jpg

The problem asks to determine the range in which 95% of the heights approximately fall, given that the heights are normally distributed with a mean of 168 cm and a standard deviation of 2.5 cm.

In a normal distribution, approximately 95% of the data falls within **two standard deviations** from the mean. This means the range can be calculated as:

\[
\text{Lower Bound} = \mu - 2 \sigma
\]
\[
\text{Upper Bound} = \mu + 2 \sigma
\]

Where:
- \(\mu = 168\) cm (the mean)
- \(\sigma = 2.5\) cm (the standard deviation)

Let's calculate this.

\[
\text{Lower Bound} = 168 - 2 \times 2.5 = 168 - 5 = 163 \, \text{cm}
\]
\[
\text{Upper Bound} = 168 + 2 \times 2.5 = 168 + 5 = 173 \, \text{cm}
\]

Thus, **95% of the heights** approximately fall within the range **163 cm to 173 cm**.

Would you like further details or have any other questions?

Here are some related questions:
1. What percentage of data falls within one standard deviation of the mean in a normal distribution?
2. How do you calculate the z-scores for values that are not exactly at the mean in a normal distribution?
3. What is the empirical rule in statistics?
4. How would the range change if we were looking for 99% of the data?
5. Can we use this normal distribution rule for non-symmetric data?

**Tip:** When solving normal distribution problems, remember the empirical rule: 68% of data lies within 1 standard deviation, 95% within 2, and 99.7% within 3.

The heights of boys in a grade 10 class are normally distributed with a mean of 168 cm and a standard deviation of 2.5 cm. In which range do 95% of the heights approximately fall?

Learn how to calculate the range in which 95% of the heights fall for a normally distributed data set. Given a mean of 168 cm and a standard deviation of 2.5 cm, this problem uses the empirical rule to determine that the range is from 163 cm to 173 cm.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation