Appendix A
Additional Problems
The problems in this document may
be used as extra review or practice for quizzes and exams. They are
organized by chapter and are very similar in spirit to those found in the
text. When referring to problems in this document, we will use the chapter
number followed by the problem number. For example, Problem 1.3 refers to
the third problem in the problem set for Chapter 1. The answers to these
problems may be found in a companion document at this website.
Problems for Chapter 3
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a. | Of the 100 members of the
U. S. Senate at the start of 2001, 50 were members of
the Republican Party and 50 were members of the Democratic
Party. Twelve senators had been elected to the national academic honor society Phi Beta
Kappa as undergraduates
in college. Four of the 12 were Republicans. If we assume that membership in Phi
BetaKappa and political affiliation are independent events,
determine the probability that:
(i)exactly 4 of the 12 are Republicans; (ii) at most 4 are Republicans. [ Based on
dataprovided by Priscilla Taylor, 2001, Personal
communication. Also see The Key Reporter
, 66 (2) : p. 4. ] |
| b. | Of the 435 members
of the U. S. House of Representatives at the start of 2001, 221
wereRepublicans. Twenty-six Representatives were
members of Phi Beta Kappa
as
undergraduates, and of these 8 were Republicans. If we
assume that membership in Phi
Beta Kappa and political affiliation are independent
events, determine the probability
that:
(i) exactly 8 of the 26 are Republicans; (ii) at
most 8 are Republicans. |
A
population has a normal distribution with mean µ = 50 and standard
deviation s = 12.
- Calculate the probability that X is greater than
54.
- Calculate the probability that X is less than 32.
- Calculate the probability that X is greater than 50
but less than 77.
- Calculate the probability that X is less than 50
but greater than 28.
- Calculate the probability that X is less than 76.
- Calculate the probability that X is greater than
33.
- Calculate the probability that X is not between 40
and 60.
- Calculate the probability that X is between 35 and
65.
- Calculate the probability that X is between 32 and
57.
- Calculate the probability that X is not between 27
and 72.
| a. | A flower of genotype Aa is self-fertilized. What is
the probability that of 10 seeds
it produces,
3 or less will have an aa genotype?
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b. | What is the probability that exactly 3 of the 10 will
have the aa genotype?
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Two
persons are on a reducing diet. The first person weighs 178 lbs and
belongs to an age and height group for which the mean weight is 144 lb
with a standard deviation of 12 lbs. The second person weighs 194 lbs and
belongs to an age and height group for which the mean weight is 160 lbs
with a standard deviation of 16 lbs. Assuming weight to be normally
distributed within each age and height group, use the Z distribution to determine which person is most
overweight. Explain your rationale.
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