Exam 2: Probability Concepts and Applications

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A probability density function is a mathematical way of describing Bayes' theorem.

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The time required to travel downtown at 10 a.m.on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes.What is the probability that it will take less than 40 minutes?

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Subjective probability assessments depend on

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If two events (A,B)are dependent,what is the conditional probability of P(A|B)?

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The probability of obtaining specific outcomes in a Bernoulli process is described by the binomial probability distribution.

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If two events (A,B)are mutually exclusive,what is the probability of event A or event B occurring?

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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?

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Properties of the normal distribution include

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Consider a standard 52-card deck of cards.The probability of drawing either a seven or a black card is 7/13.

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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?

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A company is considering producing some new Gameboy electronic games.Based on past records,management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure.Market research may be used to revise these probabilities.In the past,the successful products were predicted to be successful based on market research 90 percent of the time.However,for products that failed,the market research predicted these would be successes 20 percent of the time.If market research is performed for a new product,what is the probability that the results indicate a successful market for the product and the product actually is successful?

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The Department of Motor Vehicles (DMV)can service customers at a rate of 20 per hour (or 1/3 per minute)when it comes to license renewals.The service time follows an exponential distribution.What is the probability that it will take between 2 and 3 minutes to be served?

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If we flip a coin three times,the probability of getting three heads is 0.125.

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The standard deviation equals the square of the variance.

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Compute the F value based on the following: (a)df1 = 2,df2 = 4,α = 0.01 (b)df1 = 3 df2 = 6,α = 0.05

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Explain why event probabilities range from 0 to 1.

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Bayes' theorem is used to calculate

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A conditional probability P(B|A)is equal to its marginal probability P(B)if

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Assume that you have an urn containing 10 balls of the following description: 4 are white (W)and lettered (L) 2 are white (W)and numbered (N) 3 are yellow (Y)and lettered (L) 1 is yellow (Y)and numbered (N) If you draw a lettered ball (L),the probability that this ball is white (W)is 0.571.

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Given two statistically independent events (A,B),the joint probability of P(AB)= P(A)+ P(B).

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