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Probability Concepts and Applications test bank

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Question;2.110 An urn contains 7 blue and 3 yellow;chips. If the drawing of chips is done;with replacement, determine the probability of;(a) drawing three yellow chips;(b) drawing a blue chip on the first draw;and a yellow chip on the second draw;(c) drawing a blue chip on the second draw given that a yellow;chip was drawn on the first draw;(d) drawing a yellow chip on the second draw;given that a blue chip was drawn on the first draw;(e) drawing a yellow chip on the second draw;given that a yellow chip was drawn on the first draw;2.111 A market research study is;being conducted to determine if a product modification will be;well;received by the public. A total of 1,000;consumers are questioned regarding this product.;The;table below provides information regarding this sample.;Positive;Reaction;Neutral;Reaction;Negative;Reaction;Male;240;60;100;Female;260;220;120;(a) What is the probability that a randomly;selected male would find this change unfavorable (negative)?;(b) What is the probability that a randomly;selected person would be a female who had a positive reaction?;(c) If it is known that a person had a;negative reaction to the study, what is the probability that the person is;male?;2.112 In a production run of 300;units, there are exactly 20 defective items and 280 good items.;(a) What is the probability that a randomly;selected item is defective?;(b) If two items are sampled without;replacement, what is the probability that both are good?;(c) If two items are randomly sampled;without replacement, what is the probability that the first is good but the;second is defective?;2.113 A new television program was viewed by 200;people (120 females and 80 males). Of;the females, 60 liked the program and 60 did not. Of the males, 60 of the 80 liked the program.;(a) What is the probability that a randomly;selected individual liked the program?;(b) If a male in this group is selected;what is the probability that he liked the program?;(c) What is the probability that a randomly;selected individual is a female and liked the program?;2.114 Colonel Motors (an automobile company) has;prepared a marketing campaign for its best selling car. The focus of the campaign is quality, and it;is claimed that 97 percent of the purchasers of this car have no complaints in;the first year. You and your sister Kim;have each purchased one of these cars.;(a) What is the probability that neither of;you has a complaint about the car in the first year if the advertising claim is;true?;(b) What is the probability that exactly one;of you has a complaint about the car in the first year if the advertising claim;is true?;2.115 A local "home TV repair service;company has two repairmen who make all of the home repairs. The company sends Repairman D on 70 percent;of all jobs, because the likelihood of a "second follow-up call;within a week is only 0.08 compared to 0.20 for Repairman K. If you had a recent repair job that is going;to require a second follow-up call, what is the probability that Repairman K;did your initial repair work?;2.116 Our department store is having a sale on;personal computers, of which three are in stock (no rain checks). There is a certain probability of selling;none. The probability of selling one is;twice as great as the probability of selling none. The probability of selling two is three times;the probability of selling none. Finally;the probability of selling all the personal computers is four times as great as;the probability of selling none. In a;table, list the outcomes and their probabilities. Hint;Let the probability of selling none equal x.;2.117 ABC Manufacturing has 6 machines that perform a particular;task. Breakdowns occur frequently for;this machine. Past records indicate that;the number of breakdowns that occur each day is described by the following;probability distribution;Number of Breakdowns;Probability;0;0.4;1;0.3;2;0.2;3;0.1;More than 3;0.0;(a) What is the;expected number of breakdowns in any given day?;(b) What is the;variance for this distribution?;(c) What is the;probability that there will be at least 2 breakdowns in a day?;2.118 Fast Service Store has;maintained daily sales records on the various size "Cool Drink;sales.;Assuming;that past performance is a good indicator of future sales;?Cool Drink?;Price;Number;Sold;$0.50;75;$0.75;120;$1.00;125;$1.25;80;Total;400;(a) what is the;probability of a customer purchasing a $1.00 "Cool Drink?;(b) what is the;probability of a customer purchasing a $1.25 "Cool Drink?;(c) what is the;probability of a customer purchasing a "Cool Drink" that costs;greater than or equal to $1.00?;(d) what is the;expected value of a "Cool Drink"?;(e) what is the;variance of a "Cool Drink"?;2.119 A;southwestern tourist city has records indicating that the average daily;temperature in the summer is 82 degrees F, which is normally distributed with a;standard deviation of 3 degrees F. Based;on these records, determine;(a) the probability of a daily;temperature between 79 degrees F and 85 degrees F;(b) the probability that the daily;temperature exceeds 90 degrees F;(c) the probability that the daily;temperature is below 76 degrees F;2.120 Using the table for finding the;areas under normal curves, find the area under a normal curve with;a;mean of 200 and a standard deviation of 10 between the values of;(a) 200 to;205;(b) 195 to;205;(c) 200 to;215;(d) 195 to;215;(e) 186.5;to 217;2.121 The time required to complete a project is;known to be normally distributed with a mean of 44 weeks and a standard;deviation of 8 weeks.;(a) What is the;probability that the project is finished in 40 weeks or fewer?;(b) What is the;probability that the project is finished in 52 weeks or fewer?;(c) There is an 95 percent;chance that the project will be finished in fewer than how many weeks?;2.122 Arrivals in a university advising office;during the week of registration are known to follow a Poisson distribution with;an average of 4 people arriving each hour.;(a) What is the;probability that exactly 4 people will arrive in the next hour?;(b) What is the;probability that exactly 5 people will arrive in the next hour?;SHORT ANSWER/ESSAY;2.123 Explain why event probabilities range from;zero to one.;2.124 Using a standard deck of 52 cards, explain;why the situation of drawing a 7 and a club is not collectively exhaustive.;2.125 Name five common probability;distributions.;2.126 If two events (A,B) are mutually exclusive;what is the probability of event A or event B occurring?;2.127 If two events (A,B) are not mutually;exclusive, what is the probability of event A or event B occurring?;2.128 If two events (A,B) are;independent, what is their joint probability?;2.129 If two events (A,B) are;dependent, what is the conditional probability of P(A|B)?;2.130 If two events (A,B) are;independent, then the conditional probability of P(A|B) =;2.131 Explain what a discrete;random variable is.;2.132 The exponential;distribution often describes _______________________________.;2.133 List the two parameters of the normal distribution.;2.134 In what way is the F distribution often used?;2.135 List the parameter(s) of;the Poisson distribution.

 

Paper#60362 | Written in 18-Jul-2015

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