A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Textbook Question
Chapter 8, Problem 8.5P
Fifty numbers are rounded off to the nearest integer and then summed. If the individual round-off errors are uniformly distributed over (-.5,.5), approximate the
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Exercise 1
Mateo is the star player of a certain soccer team and is getting ready for a very important match after
spending several months recovering from an injury. If the player is injured again during this match, the
probability that his team wins is 0.32. If Mateo is not injured, the probability that his team loses is 0.18. In
addition, according to the team doctor, the probability that the player gets injured during the match is 0.15.
a. Draw a probability tree that properly represents the situation described above. Clearly label the
probabilities on each branch of the tree.
b. What is the probability that Mateo's team wins the match?
c. If Mateo's team loses the match, what is the probability that Mateo was injured?
d. Consider the event "Mateo is injured" and the event "Mateo's team wins the match." Are these events
independent? Clearly justify your answer.
A company devoted to the production and distribution of craft beer has decided to run a
quality-control check on a batch of 330 mL Porter beer bottles. A random sample of the
contents of 52 bottles was taken; the volume (in millilitres, mL) was measured and is shown
below:
Dato
Volumen
(ml)
Volumen
Volumen
Volumen
Dato
Dato
Dato
(ml)
(ml)
(ml)
333
14
326
27
330
40
329
2
328
15
331
28
329
41
327
3
335
16
331
29
329
42
323
4
330
17
333
30
332
43
330
5
331
18
332
31
334
44
332
6
326
19
327
32
336
45
333
7
330
20
330
33
328
46
328
8
329
21
328
34
326
47
329
9
332
22
325
35
330
48
327
10
334
23
330
36
332
49
331
11
333
24
334
37
333
50
333
12
336
25
332
38
331
51
328
13
327
26
325
39
334
52
336
Exercise 4
A company that manufactures engine parts has developed a new type of piston made from aluminium-
silicon alloys and other materials. The firm wishes to examine the mechanical properties of these pistons.
Specifically, it is interested in evaluating the yield strength of a piston while it is subjected to a constant
temperature of 250 °C. Here, the yield strength is the maximum stress, measured in megapascals (MPa), that
the piston can withstand before it deforms permanently.
From the first production batches, 15 pistons were randomly selected. Each was tested to determine its yield
strength (in MPa), giving the following results:
83.2, 90.1, 86.7, 102.4, 95.9, 91.3, 88.1, 84.6, 93.2, 92.6, 100.4, 86.5, 89.2, 96.8, 91.7.
Assuming that the yield strength of this type of piston follows a Normal distribution, construct a 96 %
confidence interval for the variance, σ², of the pistons' yield strength.
Chapter 8 Solutions
A First Course in Probability (10th Edition)
Ch. 8 - Suppose that X is a random variable with mean and...Ch. 8 - From past experience, a professor knows that the...Ch. 8 - Use the central limit theorem to solve part (c) of...Ch. 8 - Let X1,...,X20 be independent Poisson random...Ch. 8 - Fifty numbers are rounded off to the nearest...Ch. 8 - A die is continually rolled until the total sum of...Ch. 8 - A person has 100 light bulbs whose lifetimes are...Ch. 8 - In Problem 8.7, suppose that it takes a random...Ch. 8 - If X is a gamma random variable with parameters...Ch. 8 - Civil engineers believe that W, the amount of...
Ch. 8 - Many people believe that the daily change of price...Ch. 8 - We have 100 components that we will put in use in...Ch. 8 - Student scores on exams given by a certain...Ch. 8 - A certain component is critical to the operation...Ch. 8 - An insurance company has 10.000 automobile...Ch. 8 - A.J. has 20 jobs that she must do in sequence,...Ch. 8 - Redo Example 5b under the assumption that the...Ch. 8 - Repeat part (a) of Problem 8.2 when it is known...Ch. 8 - A lake contains 4 distinct types of fish. Suppose...Ch. 8 - If X is a nonne9ative random variable with mean...Ch. 8 - Let X be a nonnegative random variable. Prove that...Ch. 8 - Prob. 8.22PCh. 8 - Let X be a Poisson random variable with mean 20....Ch. 8 - Prob. 8.24PCh. 8 - Prob. 8.25PCh. 8 - If f(x) is an Increasing and g(x) is a decreasing...Ch. 8 - If L(p) is the Lorenz curve associated with the...Ch. 8 - Suppose that L(p) is the Lorenz curve associated...Ch. 8 - If X has variance 2, then , the positive square...Ch. 8 - If X has mean and standard deviation , the ratio...Ch. 8 - Compute the measurement signal-to-noise ratio-that...Ch. 8 - Let Zn,n1, be a sequence of random variables and...Ch. 8 - Prob. 8.5TECh. 8 - Prob. 8.6TECh. 8 - Prob. 8.7TECh. 8 - Explain why a gamma random variable with...Ch. 8 - Prob. 8.9TECh. 8 - If X is a Poisson random variable with mean , show...Ch. 8 - Prob. 8.11TECh. 8 - Prob. 8.12TECh. 8 - Prob. 8.13TECh. 8 - Prob. 8.14TECh. 8 - If f and g are density functions that are positive...Ch. 8 - Prob. 8.16TECh. 8 - The number of automobiles sold weekly at a certain...Ch. 8 - Prob. 8.2STPECh. 8 - If E[X]=75E[Y]=75Var(X)=10var(Y)=12cov(X,Y)=3 give...Ch. 8 - Prob. 8.4STPECh. 8 - Prob. 8.5STPECh. 8 - Prob. 8.6STPECh. 8 - Prob. 8.7STPECh. 8 - Prob. 8.8STPECh. 8 - Prob. 8.9STPECh. 8 - A tobacco company claims that the amount of...Ch. 8 - Prob. 8.11STPECh. 8 - Prob. 8.12STPECh. 8 - The strong law of large numbers states that with...Ch. 8 - Each new book donated to a library must be...Ch. 8 - Prove Chebyshevs sum inequality, which says that...
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