Name _________________________________
Period _________________
Special Topics 8.4
Empirical Rule Practice
1.
Assume that the heights of college women are normally distributed, with mean 65 in. and standard
deviation 2.5 in.
a.
b.
c.
d.
e.
f.
g.
What percentage of women are taller than 65 in.?
What percentage of women are shorter than 65 in.?
What percentage of women are between 62.5 in. and 67.5 in.?
What percentage of women are between 60 in. and 70 in.?
What percentage of women are between 60 and 67.5 in?
What percentage of women are shorter than 70 in.?
Approximately how tall would a woman need to be in order to be located in the 50 th percentile?
97th percentile?
2. The incubation time for Rhode Island Red chicks is normally distributed with mean 21 days and standard
deviation approximately 1 day. If 1000 eggs are being incubated, how many chicks do we expect will
hatch
a.
b.
c.
d.
In 19 to 23 days?
In 21 days or fewer?
In 19 days or fewer
In 18 to 24 days?
e. In 22 days or more?
f. In 18 to 21 days?
g. In 19 to 24 days?
h. In 18 days or more?
3. At Burnt Mesa Pueblo, archaeological studies have used the method of tree ring dating in an effort to
determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of
(year) 1243 with standard deviation 36 years. The distribution of dates was normal.
a.
Estimate the range of years centered about the mean in which about 68% of the data will be
found.
b. Estimate a range of years centered about the mean in which about 95% of the data will be found.
c. Estimate a range of years that the lower 16% of the data will be found.
d. Estimate a range of years that the upper 2.5% of the data will be found.
e. Estimate a range of years centered about the mean in which almost all of the data will be found.
4. A vending machine automatically pours soft drinks into cups. The amount of soft drink dispensed into a
cup is normally distributed with mean 7.6 oz and standard deviation of 0.4 oz.
a. Estimate the probability that the machine will over flow an 8-oz cup.
b. Estimate the probability that the machine will not over flow an 8-oz cup.
c. The machine has just been loaded with 850 cups. How many of these do you expect will overflow
when served?
5. The average reading speed of students completing a speed-reading course is 450 words per minute (wpm)
with standard deviation of 70 wpm. N(450,70)
a) Draw and label the appropriate normal distribution.
b) What percent of the students read between 380 and 520 wpm?
c) What percent of the students read slower than 310 wpm?
d) What percent of the students read between 310 and 590 wpm?
e) What percent of the students read between 380 and 590 wpm?
f) A reading speed of 520 wpm would be in what percentile?
g) Does the 68-95-99.7 rule allow us to find the percent readers that read 500 wpm or less?
Explain.
6. Given that the scores on a test are normally distributed, that the mean score is 80 and the
standard deviation is 7,
1. What percent scored less than 87?
2. What percent scored less than 73?
3. What percent scored more than 94?
4. 2.5% scored less than what value.
7. Given the times required for a group of students to complete the physical fitness obstacle course
result in a normal curve, and that the mean time 21 minutes and the standard deviation is 4,
1. What percent took longer than 29 minutes?
2. What percent took less than 29 minutes?
3. What percent took between 13 and 29 minutes?
4. What percent took between 13 and 25 minutes?
5. What percent took longer than 17 minutes?