The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score for a university is 522. Assume that GMAT scores are bell-shaped with a standard deviation of 100.

If required, round your answers to one decimal place.

Given the dataGiven the 

- **Mean** (\(\mu\)) = 522
- **Standard deviation** (\(\sigma\)) = 100

The GMAT scores follow a bell-shaped (normal) distribution. Based on this, we can apply the empirical rule (also known as the 68-95-99.7 rule), which tells us how much data lies within certain standard deviations from the mean in a normal distribution:

1. **Within 1 standard deviation (\(\mu \pm \sigma\))**: Approximately 68% of the data falls within 1 standard deviation of the mean.
2. **Within 2 standard deviations (\(\mu \pm 2\sigma\))**: Approximately 95% of the data falls within 2 standard deviations of the mean.
3. **Within 3 standard deviations (\(\mu \pm 3\sigma\))**: Approximately 99.7% of the data falls within 3 standard deviations of the mean.

Let's calculate the ranges for each:

1. **Within 1 standard deviation**:  
   \[
   522 - 100 = 422 \quad \text{to} \quad 522 + 100 = 622
   \]
   So, approximately 68% of scores are between 422 and 622.

2. **Within 2 standard deviations**:  
   \[
   522 - 200 = 322 \quad \text{to} \quad 522 + 200 = 722
   \]
   So, approximately 95% of scores are between 322 and 722.

3. **Within 3 standard deviations**:  
   \[
   522 - 300 = 222 \quad \text{to} \quad 522 + 300 = 822
   \]
   So, approximately 99.7% of scores are between 222 and 822.

These ranges help visualize where most students' GMAT scores will lie. If you need to calculate specific probabilities or percentiles, we can use a standard normal distribution (z-scores).

Would you like further details or clarifications? Here are 5 related questions:

1. What percentage of GMAT scores would be above 622?
2. How can you calculate the probability of a GMAT score below 400?
3. What score corresponds to the 90th percentile of this distribution?
4. How would we find the z-score for a GMAT score of 650?
5. If a score of 700 is considered excellent, how many standard deviations above the mean is it?

**Tip**: In a normal distribution, z-scores are used to determine how many standard deviations away from the mean a particular value lies.

The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score for a university is 522. Assume that GMAT scores are bell-shaped with a standard deviation of 100. If required, round your answers to one decimal place.

Understand the normal distribution of GMAT scores with a mean of 522 and a standard deviation of 100. Learn how to apply the empirical rule to calculate score ranges within 1, 2, and 3 standard deviations of the mean. This problem is ideal for high school students in Grades 10-12.

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