Chapter 19 Deviation from the Mean820
Problems for Section 19.3
Practice Problems
Problem 19.5.
Suppose 120 students take a final exam and the mean of their scores is 90. You
have no other information about the students and the exam, that is, you should not
assume that the highest possible score is 100. You may, however, assume that exam
scores are nonnegative.
(a)State the best possible upper bound on the number of students who scored at
least 180.
(b)Now suppose somebody tells you that the lowest score on the exam is 30.
Compute the new best possible upper bound on the number of students who scored
at least 180.
Problem 19.6.
Suppose you flip a fair coin 100 times. The coin flips are all mutually independent.
(a)What is the expected number of heads?(b)What upper bound on the probability that the number of heads is at least 70
can we derive using Markov’s Theorem?
(c)What is the variance of the number of heads?(d)What upper bound does Chebyshev’s Theorem give us on the probability that
the number of heads is either less than 30 or greater than 70?
Problem 19.7.
Tom has a gambling problem. He plays 240 hands of draw poker, 120 hands of
black jack, and 40 hands of stud poker per day. He wins a hand of draw poker with
probability 1/6, a hand of black jack with probability 1/2, and a hand of stud poker
with probability 1/5.
(a)What is the expected number of hands that Tom wins in a day?(b)What would the Markov bound be on the probability that Tom will win at least
216 hands on a given day?