https://file.aiquickdraw.com/mathbot/file/1726520596115x9qm0x2g.jpg

The given image contains a problem regarding the scores of the GRE Chemistry test, which are normally distributed with a mean of 694 and a standard deviation of 112. The problem is split into two parts:

### (a) Approximate percentage of test takers scoring 900 or above:
To solve this, we need to find the percentage of people scoring greater than or equal to 900. This requires calculating the **z-score** and using the **standard normal distribution**.

The formula for the **z-score** is:

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

Where:
- \(x = 900\) (the score we are investigating),
- \(\mu = 694\) (the mean),
- \(\sigma = 112\) (the standard deviation).

Let's calculate the z-score and then use standard normal distribution tables or a calculator to find the percentage of scores greater than this z-score.

### (b) Estimate the 99th percentile score:
For this, we need to find the score corresponding to the 99th percentile. The z-score for the 99th percentile in a standard normal distribution is approximately **2.33**. We can use the formula for converting a z-score back to a raw score:

\[
x = \mu + z \cdot \sigma
\]

Where \(z = 2.33\), \(\mu = 694\), and \(\sigma = 112\).

Let's calculate both parts. I'll compute them now.### Results:

(a) Approximately **3.29%** of test takers score greater than or equal to 900 on the GRE Chemistry test.

(b) The score corresponding to the 99th percentile is approximately **954.96**.

Would you like more details or have any questions?

Here are some related questions you might find helpful:
1. How do you interpret the z-score in statistics?
2. What is the significance of percentiles in standardized tests?
3. How is the normal distribution used in analyzing exam scores?
4. What would the 95th percentile score be for this distribution?
5. How can you calculate the percentage for any arbitrary score using the normal distribution?

**Tip:** When dealing with normal distributions, always check if the given data is actually normally distributed, as this can impact the accuracy of percentile-based calculations.

The scores on the GRE Chemistry test are normally distributed with a mean of 694 and a standard deviation of 112. (a) What percentage of test takers earn a score greater than or equal to 900? (b) Estimate the 99th percentile score on the GRE Chemistry test.

Learn how to calculate the percentage of GRE Chemistry test takers who score above 900 and estimate the 99th percentile score, using the standard normal distribution, mean, and standard deviation. This problem covers concepts like z-scores and percentile calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation