# k12.org exercise: Standard normal distribution and the empirical | Khan Academy | Summary and Q&A

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January 8, 2010
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k12.org exercise: Standard normal distribution and the empirical | Khan Academy

## TL;DR

The video discusses a problem involving the normal distribution and applies the empirical rule to determine the percentage of data and order the given values.

## Questions & Answers

### Q: What is the mean of a standard normal distribution?

The mean of a standard normal distribution is 0.

### Q: How can the empirical rule be used to estimate percentages under a normal distribution?

The empirical rule states that approximately 68% of data falls within one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations. By using this rule, you can estimate percentages without a normal distribution table.

### Q: What is the percentage of data below 1 in a standard normal distribution?

Using the empirical rule, the area under the bell curve up to 1 is approximately 68%. This is because 68% of data falls within one standard deviation of the mean.

### Q: How can we determine the percentage of data above 2 in a standard normal distribution?

By applying the empirical rule, we find that 95% of data falls within two standard deviations of the mean. Therefore, the remaining area beyond two standard deviations is 5%, which is divided equally on both tails, giving us 2.5% for the percentage of data above 2.

## Summary & Key Takeaways

• The video introduces problem number 4 from a free AP Statistics FlexBook by ck12.org.

• It explains how to draw a standard normal distribution and identifies the mean as 0 and the standard deviation as 1.

• The video demonstrates how to use the empirical rule to calculate the percentage of data and order the given values.