Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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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
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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) =
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) What is ??
b) Write out the formula for the probability distribution of the random variable r. P(r) = _________
c) Find the probability that one otter will initiate social grooming four or more times during the 30-minute observation period. (Round your answer to four decimal places.)
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
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...
Ch. 2.2 - A mutual fund company offers its customers a...Ch. 2.2 - Consider randomly selecting a student at a large...Ch. 2.2 - A computer consulting firm presently has bids out...Ch. 2.2 - Suppose that 55% of all adults regularly consume...Ch. 2.2 - Consider the type of clothes dryer (gas or...Ch. 2.2 - An individual is presented with three different...Ch. 2.2 - Let A denote the event that the next request for...Ch. 2.2 - A wallet contains five 10 bills, four 5 bills, and...Ch. 2.2 - Human visual inspection of solder joints on...Ch. 2.2 - A certain factory operates three different shifts....Ch. 2.2 - An insurance company offers four different...Ch. 2.2 - The route used by a certain motorist in commuting...Ch. 2.2 - The computers of six faculty members in a certain...Ch. 2.2 - Show that if one event A is contained in another...Ch. 2.2 - The three most popular options on a certain type...Ch. 2.2 - A certain system can experience three different...Ch. 2.2 - An academic department with five faculty members...Ch. 2.2 - In Exercise 5, suppose that any incoming...Ch. 2.3 - As of April 2006, roughly 50 million .com web...Ch. 2.3 - A friend of mine is giving a dinner party. His...Ch. 2.3 - The composer Beethoven wrote 9 symphonies, 5 piano...Ch. 2.3 - An electronics store is offering a special price...Ch. 2.3 - Again consider a Little League team that has 15...Ch. 2.3 - Computer keyboard failures can be attributed to...Ch. 2.3 - A production facility employs 10 workers on the...Ch. 2.3 - An academic department with five faculty members...Ch. 2.3 - An experimenter is studying the effects of...Ch. 2.3 - A sonnet is a 14-line poem in which certain...Ch. 2.3 - A box in a supply room contains 15 compact...Ch. 2.3 - Three molecules of type A, three of type B, three...Ch. 2.3 - An ATM personal identification number (PIN)...Ch. 2.3 - A starting lineup in basketball consists of two...Ch. 2.3 - In five-card poker, a straight consists of five...Ch. 2.3 - Show that (nk)=(nnk). Give an interpretation...Ch. 2.4 - The population of a particular country consists of...Ch. 2.4 - Suppose an individual is randomly selected from...Ch. 2.4 - Return to the credit card scenario of Exercise 12...Ch. 2.4 - Reconsider the system defect situation described...Ch. 2.4 - The accompanying table gives information on the...Ch. 2.4 - A department store sells sport shirts in three...Ch. 2.4 - According to a July 31, 2013, posting on cnn.com...Ch. 2.4 - A system consists of two identical pumps, #1 and...Ch. 2.4 - A certain shop repairs both audio and video...Ch. 2.4 - In Exercise 13, Ai = {awarded project i}, for i =...Ch. 2.4 - Deer ticks can be carriers of either Lyme disease...Ch. 2.4 - For any events A and B with P(B) 0, show that...Ch. 2.4 - If P(B|A) P(B), show that P(B|A) P(B). [Hint:...Ch. 2.4 - Show that for any three events A, B, and C with...Ch. 2.4 - At a certain gas station, 40% of the customers use...Ch. 2.4 - Seventy percent of the light aircraft that...Ch. 2.4 - Components of a certain type are shipped to a...Ch. 2.4 - Blue Cab operates 15% of the taxis in a certain...Ch. 2.4 - For customers purchasing a refrigerator at a...Ch. 2.4 - The Reviews editor for a certain scientific...Ch. 2.4 - A large operator of timeshare complexes requires...Ch. 2.4 - Consider the following information about travelers...Ch. 2.4 - There has been a great deal of controversy over...Ch. 2.4 - A friend who lives in Los Angeles makes frequent...Ch. 2.4 - In Exercise 59, consider the following additional...Ch. 2.5 - Reconsider the credit card scenario of Exercise 47...Ch. 2.5 - An oil exploration company currently has two...Ch. 2.5 - In Exercise 13, is any Ai independent of any other...Ch. 2.5 - If A and B are independent events, show that A and...Ch. 2.5 - The proportions of blood phenotypes in the U.S....Ch. 2.5 - One of the assumptions underlying the theory of...Ch. 2.5 - In October, 1994, a flaw in a certain Pentium chip...Ch. 2.5 - An aircraft seam requires 25 rivets. The seam will...Ch. 2.5 - A boiler has five identical relief valves. The...Ch. 2.5 - Two pumps connected in parallel fail independently...Ch. 2.5 - Consider the system of components connected as in...Ch. 2.5 - Refer back to the series-parallel system...Ch. 2.5 - Consider independently rolling two fair dice, one...Ch. 2.5 - Components arriving at a distributor are checked...Ch. 2.5 - Prob. 84ECh. 2.5 - A quality control inspector is examining newly...Ch. 2.5 - a. 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. A certain company sends 40% of its overnight...Ch. 2 - A company uses three different assembly linesA1,...Ch. 2 - Disregarding the possibility of a February 29...Ch. 2 - One method used to distinguish between granitic...Ch. 2 - A subject is allowed a sequence of glimpses to...Ch. 2 - In a Little League baseball game, team As pitcher...Ch. 2 - Four engineers, A, B, C, and D, have been...Ch. 2 - A particular airline has 10 a.m. flights from...Ch. 2 - Consider four independent events A1, A2, A3, and...Ch. 2 - A box contains the following four slips of paper,...Ch. 2 - Show that if A1, A2, and A3 are independent...
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- A gender psychologist is interested in studying whether children, when left on their own, actually show more interest in toys associated with their assigned gender. The psychotherapist allows the participants (n = 16) to move freely back and forth for 40 minutes between two rooms, one of which contains toys traditionally associated with girls and another which contains toys traditionally associated with boys. She collects the data and finds that on average the children spend 23 minutes in the room (M = 23) with the toys associated with their assigned gender, with a standard deviation of s = 9. She conducts a one-tailed test and sets the alpha at .05. The alternative hypothesis is μ > ______ What is the critical t? _________ Calculate the t value and round to 2 decimals: _______ With alpha = .05. can she reject the null (type yes or no)? _______arrow_forwardSuppose 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 did not travel as far as 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 21 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 п P 185 21 -0.65 0.262 The results statistically significant at a = 0.05 because P 0.05. are are not >arrow_forwardA seamstress works exclusively on one stage of the process of a special garment design. This phase requires exactly half an hour to finish the garment. Every 30 minutes an assistant arrives at the seamstress's table to collect those finished garments and deliver those that require the process (unprocessed garments).The number of raw garments brought by the assistant to the seamstress is uncertain; 30% of the occasions arrive without garments; 50% of the time he wears one garment and 20% of the time he wears 2 garments. The assistant is instructed that there are never more than three unprocessed garments left on the seamstress's table (those that cannot be left are taken to another seamstress). Determine the transition graph and matrix that models the number of raw garments on the seamstress's table just before the assistant arrives.arrow_forward
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