Name _______________
Period ____ Date ______
Chapter 5 Review Worksheet
Directions: Please complete the worksheet to the best of your ability. Please use a
separate sheet of paper.
1. Draw the normal distribution for the following situations. Label the mean and
three standard deviations on either side of the mean.
a. In the commercial production of eggs, breakage is a major problem.
Consequently, the thickness of the eggs produced by a large flock of
White Leghorn hens were observed to follow approximately a normal
distribution with a mean μ = 0.38 mm and standard deviation σ = 0.003
mm.
b. In certain nerve cells, spontaneous electrical discharges are observed that
are so rhythmically repetitive that they are called “clock-spikes.” The
timing of these spikes, even though remarkably regular, does exhibit
variation. In one study, the interspike-time intervals (in milliseconds) for a
single housefly (Musca domestica) were observed to follow approximately
a normal distribution with mean μ = 15.6 ms and standard deviation σ =
0.4 ms1.
c. When a certain electronic instrument is used for counting particles such as
white blood cells, the measurement error distribution is approximately
normal. For white blood cells, the standard deviation of repeated counts
based on the same blood specimen is about 1.4% of the true count. Thus,
if the true count of a certain blood specimen were 7,000 cells/mm2, then
the standard deviation would be about 100 cells/mm2.
2. Suppose a certain population of observations is normally distributed. What
percentage of the observations in the population (HINT: use μ = 0 and σ = 1)
a. Are within ±1.5 standard deviations of the mean?
b. Are more than 2.5 standard deviations of the mean?
c. Are more than ±3.5 standard deviations of the mean?
1
Hengstenberg, R. (1971). Das Augenmuskelsystem der Stubenfliege Musca domestica.
1. Analyse der “clock-spikes” und ihrer Quellen. KybernetikI 2, 56-57.
2
Adapted from Magath, T. B., and Betkson, J. (1960). Electronic Blood-cell counting.
American Journal of Clinical Pathology 34, 203-213.
3. The brain weights of a certain population of adult Swedish males follow
approximately a normal distribution with mean 1,400 g and standard deviation
100g3. What percentage of the brain weights are
a. 1,500 g or less?
b. Between 1,325 and 1,500 g?
c. 1,325 g or more?
d. 1,475 g or more?
e. Between 2,475 and 1,600 g?
f. Between 1,200 and 1,325 g?
4. Let x represent a brain weight randomly chosen from the population of #3. Find
a. P(x < 1,325)
b. P(1,475 < x < 1,600)
5. In an agricultural experiment, a large uniform field was planted with a single
variety of wheat. The field was divided into many plots (each plot being 7 x 100
ft) and the yield (lb) of grain was measured for each plot. These plot yields
followed approximately a normal distribution with mean 88 lb and standard
deviation 7lb.4 For the wheat-yield distribution find
a. 80 lb or more?
b. 90 lb or more?
c. 75 lb or less?
d. Between 75 and 90 lb?
e. Between 90 and 100 lb?
f. Between 75 and 80 lb?
6. Refer to #5. Let x represent the yield of a plot chosen at random from the field.
Find
a. P(x > 90)
b. P(75 < x < 90)
7. Consider a standard normal distribution, Z. Find
a. z0.10
b. z0.25
c. z0.05
d. z0.01
8. For the wheat-yield distribution of #5, find
a. The 65th percentile
b. The 35th percentile
3
Adapted from Pearl, R. (1905). Biometrical studies on man. I. Variation and correlation
in brain weight. Biometrika 4, 13-104.
4
Adapted from Swearingen, M.L., and Halt, D.A. (1976). Using a “blank” trial as a
teaching tool. Journal of Agronomic Education 5, 3-8.
9. The serum cholesterol levels of 12- to 14-year-olds follow a normal distribution
with mean 162 mg/dl and standard deviation of 28 mg/dl. What percentage of 12to 14-year-olds have serum cholesterol values
a. 171 or more?
b. 143 or less?
c. 194 or less?
d. 105 or more?
e. Between 166 and 194?
f. Between 105 and 138?
g. Between 138 and 166?
10. Refer to #9. Suppose a 13-year-old is chosen at random and let x be the person’s
serum cholesterol value. Find
a. P( x > 166)
b. P(166 < x < 194)
11. For the serum cholesterol distribution of #9, find
a. The 80th percentile
b. The 20th percentile
12. The amount of growth, in a 15-day period, for a population of sunflower plants
was found to follow a normal distribution with mean 3.18 cm and standard
deviation 0.53 cm.5 What percentage of plants grow
a. 4 cm or more?
b. 3 cm or less?
c. Between 2.5 and 3.5 cm?
13. Refer to #12. In what range do the middle 90% of all growth values lie?
14. For the sunflower plant growth distribution of #12, what is the 25th percentile?
15. The shell thicknesses of the eggs produced by large flock of hens follow
approximately a normal distribution with mean equal to 0.38 mm and standard
deviation equal to 0.03 mm. Find the 95th percentile of the thickness distribution.
16. The intelligence quotient (IQ) score, as measured by the Stanford-Binet IQ test, is
normally distributed in certain population of children. The mean IQ score is 100
points, and the standard deviation is 16 points.6 What percentage of children in
the population have IQ scores
a. 140 or more?
b. 80 or less?
5
Unpublished data courtesy of Susan Whitehead, Oberlin College.
This is standard reference distribution for Stanford-Binet scores. See Sattler, J.M.
(1982). Assessment of Children’s Intelligence and Special Abilities, 2nd ed. Boston: Allyn
and Bacon. p. 19 and back cover
6
c. Between 80 and 120?
d. Between 80 and 140?
e. Between 120 and 140?
17. Refer to the IQ distribution of #16. Let x be the IQ score of a child chosen at
random from the population. Find P( 80 < x < 140).
18. The heights of a certain population of corn plants follow a normal distribution
with mean 145 cm and standard deviation of 22 cm. 7 What percentage of the
plant heights are
a. 100 cm or more?
b. 120 cm or less?
c. Between 120 and 150 cm?
d. Between 100 and 120 cm?
e. Between 150 and 180 cm?
f. 180 cm or more?
g. 150 cm or less?
19. Refer to the corn plant population of #18. Find the 90th percentile of the height
distribution.
20. Using a normal distribution with a mean of 0 and standard deviation of 1. State
the percentage of values that are within
a. ± 1 standard deviation of the mean
b. ± 2 standard deviations of the mean
c. ± 3 standard deviations of the mean
7
Fictitious but realistic population, based on data of Emerson, R.A., and East, E.M.
(1913). Inheritance of quantitative character in maize. Nebraska Experimental Station
Research Bulletin 2. Data reproduced by Mather, K. (1943). Statistical Analysis in
Biology. London: Methuen. pp. 29, 34. Modern hybrid corn in taller and less variable
than this population.