Chapter 6, Problem 13SE

Applying the Empirical Rule with z-Scores The Empirical Rule applies rough approximations to probabilities for any unimodal, symmetric distribution. But for the Normal distribution we can be more precise. Use the figure and the fact that the Normal curve is symmetric to answer the questions. Do not use a Normal table or technology.

According to the Empirical Rule,

a. Roughly what percentage of $z$ -scores are between $-2$ and 2?

i. almost all ii. 95%

iii. 68% iv. 50%

b. Roughly what percentage of $z$ -scores are between $-3$ and 3?

i. almost all ii. 95%

iii. 68% iv. 50%

c. Roughly what percentage of $z$ -scores are between $-1$ and 1.

i. almost all ii. 95%

iii. 68% iv. 50%

d. Roughly what percentage of $z$ -scores are greater than 0?

i. almost all ii. 95%

iii. 68% iv. 50%

e. Roughly what percentage of $z$ -scores are between 1 and 2?

i. almost all ii. 13.5%

iii. 50% iv. 2%