New Zealand
Level 7 - NCEA Level 2

# 68-95-99.7 Rule (empirical rule)

## Interactive practice questions

Complete the following statements for a normal distribution using the empirical rule.

a

$\editable{}$$%% of the scores lie within 11 standard deviation of the mean. b \editable{}$$%$% of the scores lie within $2$2 standard deviations of the mean.

c

$\editable{}$$%$% of the scores lie within $3$3 standard deviations of the mean.

Easy
Approx a minute

In a normal distribution, what percentage of scores lie between the mean and $1$1 standard deviation above the mean? Use the empirical rule to find your answer.

In a normal distribution, what percentage of scores lie between the mean and $2$2 standard deviations below the mean? Use the empirical rule to find your answer.

In a normal distribution, what percentage of scores lie between the mean and $3$3 standard deviations below the mean? Use the empirical rule to find your answer.

### Outcomes

#### S7-4

S7-4 Investigate situations that involve elements of chance: A comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions B calculating probabilities, using such tools as two-way tables, tree diagrams, simulations, and technology.

#### 91267

Apply probability methods in solving problems