TC3 → Stan Brown → Statistics → 68-95-99.7 Practice
revised 16 Feb 2008

# Empirical Rule Practice Problems

1. What percent of a normal population is more than 2 standard deviations above the mean?
P( z > 2 ) =

Data for
the rest:
Adult women’s heights are ND (normally distributed) with μ = 65.5 in (5′5½″) and σ = 2.5 in.
1′ = 12″ (one foot = 12 inches)

2. What percent of adult women have heights between 65.5 and 68 in (5′5½″ and 5′8″)?
P( 65.5 ≤ x ≤ 68 ) =

3. What proportion of adult women have heights greater than 70.5 in (5′10½″)?
P( x > 70.5 ) =

4. What’s the probability that a randomly selected adult woman is less than 63 in tall (5′3″)?
P( x < 63 ) =

5. If a woman is 68 in (5′8″) tall, what’s her percentile rank?
P( x _____ 68 ) =

6. What’s the area under the curve between 58 in and 68 in (4′10″ and 5′8″)?
P( 58 < x < 68 ) =

7. What proportion of adult women are between 5′5½″ and 5′6½″?
P( 65.5 ≤ x ≤ 66.5 ) =

This page is used in instruction at Tompkins Cortland Community College in Dryden, New York; it’s not an official statement of the College. Please visit www.tc3.edu/instruct/sbrown/ to report errors or ask to copy it.

For updates and new info, go to http://www.tc3.edu/instruct/sbrown/stat/