Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Textbook Question
Chapter 2.5, Problem 81E
Refer back to the series-parallel system configuration introduced in Example 2.36, and suppose that there are only two cells rather than three in each parallel subsystem [in Figure 2.14(a), eliminate cells 3 and 6, and renumber cells 4 and 5 as 3 and 4]. Using P(Ai) = .9, the probability that system lifetime exceeds t0 is easily seen to be .9639. To what value would .9 have to be changed in order to increase the system lifetime reliability from .9639 to .99? [Hint: Let P(Ai) = p, express system reliability in terms of p, and then let x = p2.]
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In his doctoral thesis, L. A. Beckel (University of Minnesota, 1982) studied the social behavior of river otters during the mating season. An important role in the bonding process of river otters is very short periods of social grooming. After extensive observations, Dr. Beckel found that one group of river otters under study had a frequency of initiating grooming of approximately 1.7 for each 10 minutes. Suppose that you are observing river otters for 40 minutes. Let r = 0, 1, 2, ... be a random variable that represents the number of times (in a 40-minute interval) one otter initiates social grooming of another.
Lambda = 6.8
(b) Find the probabilities that in your 40 minutes of observation, one otter will initiate social grooming four times, five times, and six times. (Round your answers to four decimal places.)
P(4) =
P(5) =
P(6) =
Suppose Aaron recently purchased an electric car. The person who sold him his new car told him that he could consistently
travel 200 mi before having to recharge the car's battery. Aaron began to believe that the car traveled even farther than the
company claimed, and he decided to test this hypothesis formally. Aaron drove his car only to work and he recorded the
number of miles that his new car traveled before he had to recharge its battery a total of 17 separate times. The table shows
the summary of his results. Assume his investigation satisfies all conditions for a one-sample t-test.
Mean miles traveled Sample size t-statistic P-value
P
207
17
1.48
0.079
The results
statistically significant at a = 0.01 because P
0.01.
are
are not
V
In his doctoral thesis, L. A. Beckel (University of Minnesota, 1982) studied the social behavior of river otters during the mating season. An important role in the bonding process of river otters is very short periods of social grooming. After extensive observations, Dr. Beckel found that one group of river otters under study had a frequency of initiating grooming of approximately 1.7 for each 10 minutes. Suppose that you are observing river otters for 30 minutes. Let r = 0, 1, 2, ... be a random variable that represents the number of times (in a 30-minute interval) one otter initiates social grooming of another.
a) Find the probabilities that in your 30 minutes of observation, one otter will initiate social grooming four times, five times, and six times. (Round your answers to four decimal places.)
P(4) =
P(5) =
P(6) =
b) Find the probability that one otter will initiate social grooming less than four times during the 30-minute observation period. (Round your answer…
Chapter 2 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 2.1 - Four universities1, 2, 3, and 4are participating...Ch. 2.1 - Suppose that vehicles taking a particular freeway...Ch. 2.1 - Three components are connected to form a system as...Ch. 2.1 - Each of a sample of four home mortgages is...Ch. 2.1 - A family consisting of three personsA, B, and...Ch. 2.1 - A college library has five copies of a certain...Ch. 2.1 - An academic department has just completed voting...Ch. 2.1 - An engineering construction firm is currently...Ch. 2.1 - Use Venn diagrams to verify the following two...Ch. 2.1 - a. In Example 2.10, identify three events that are...
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A lumber company has just taken delivery on a...Ch. 2.5 - Consider randomly selecting a single individual...Ch. 2.5 - The probability that an individual randomly...Ch. 2.5 - Suppose identical tags are placed on both the left...Ch. 2 - A certain legislative committee consists of 10...Ch. 2 - A factory uses three production lines to...Ch. 2 - An employee of the records office at a certain...Ch. 2 - One satellite is scheduled to be launched from...Ch. 2 - A transmitter is sending a message by using a...Ch. 2 - Individual A has a circle of five close friends...Ch. 2 - According to the article Optimization of...Ch. 2 - A chemical engineer is interested in determining...Ch. 2 - Prob. 98SECh. 2 - Fasteners used in aircraft manufacturing are...Ch. 2 - Jay and Maurice are playing a tennis match. In one...Ch. 2 - A system consists of two components. The...Ch. 2 - The accompanying table categorizing each student...Ch. 2 - a. 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