Question

103 - empirical rule and normal distribution extra practice
name janya
date
in a normal distribution, what percent of the values lie:

1. below the mean? 2. above the mean? 3. within one standard

deviation of the mean?

1. within two standard deviations of the mean?
2. within three standard deviations of the mean?

Explanation:

Step1: Recall properties of normal distribution

A normal distribution is symmetric about the mean. So, half of the data is below the mean and half is above.

Step2: Apply empirical rule (68 - 95 - 99.7 rule)

• For one - standard deviation: Approximately 68% of the data lies within \( \mu\pm\sigma\) (where \(\mu\) is the mean and \(\sigma\) is the standard deviation).
• For two - standard deviations: Approximately 95% of the data lies within \( \mu\pm2\sigma\).
• For three - standard deviations: Approximately 99.7% of the data lies within \( \mu\pm3\sigma\).

Answer:

1. 50%
2. 50%
3. 68%
4. 95%
5. 99.7%