Exam 2: Probability Concepts and Applications

A discrete random variable has a mean of 400 and a variance of 64.What is the standard deviation?

The time required to complete a project is normally distributed with a mean of 80 weeks and a standard deviation of 10 weeks.The construction company must pay a penalty if the project is not finished by the due date in the contract.If a construction company bidding on this contract wishes to be 90 percent sure of finishing by the due date, what due date (project week #)should be negotiated?

Suppose that 10 sophomores enter a belching contest and that their respective skill levels are approximately the same.Six of the entrants are female and two of those are engineering majors.Three of the men are engineers.What is the probability that the winner will be a male engineering major?

Suppose that we determine the probability of a warm winter based on the number of warm winters experienced over the past 10 years.In this case, we have used

A production process is known to produce a particular item in such a way that 5 percent of these are defective.If two items are randomly selected as they come off the production line, what is the probability that the second item will be defective?

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.

A call center receives calls from customers at a rate of 2 per min.The time between customer calls follows an exponential distribution. (a)What is the probability that it takes 1/3 of a minute or less between consecutive customer calls? (b)What is the probability that it takes 1/2 of a minute or more between consecutive customer calls?

If P(A)= 0.3, P(B)= 0.2, P(A and B)= 0.0, what can be said about events A and B?

"It's 75 degrees and sunny here in San Diego this afternoon...," the weatherman droned on, repeating a phrase that probably should have been recorded and played on an endless loop.Tim looked at the previous year's high temperatures and noted that the average was 75 degrees with a standard deviation of 2.5 degrees and approximated a normal distribution.Armed with this evidence, determine: (a)the probability of a daily temperature between 79 degrees F and 85 degrees F. (b)the probability that the daily temperature exceeds 80 degrees F. (c)the probability that the daily temperature is below 74 degrees F.

Disco Fever is randomly found in one half of one percent of the general population.Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease.The test also yields a false-positive in 4% of the cases where the disease is not present.What is the probability that the disease is present if the test result comes back positive?

The F distribution is a continuous probability distribution that is helpful in testing hypotheses about variances.

Given two statistically dependent events (A,B), the conditional probability of P(A|B)= P(B)/P(AB).

Disco Fever is randomly found in one half of one percent of the general population.Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease.The test also yields a false-positive in 4% of the cases where the disease is not present.What is the probability that the disease is absent if the test result is negative?

An MBA director has decided to improve the profile of her program by admitting only the finest students.After an exhaustive search on the internet, she learns that combined GMAT scores average 550 with a standard deviation of 130. (a)What cutoff score should she establish if she wants to consider only applicants scoring in the top 5%? (b)If she uses 700 as her minimum score, what percentile can she claim for her incoming class' performance on the GMAT? (c)If 1000 test takers apply, would she expect to find more students with scores in the range of 500 to 600 or in the range of 50 to 450? (Assume that applicants can actually score a 50 on the GMAT.)

At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course.Of these 200 students, 50 are also enrolled in an introductory accounting course.There are an additional 250 business students enrolled in accounting but not enrolled in statistics.If a business student is selected at random, what is the probability that the student is not enrolled in statistics?

At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course.Of these 200 students, 50 are also enrolled in an introductory accounting course.There are an additional 250 business students enrolled in accounting but not enrolled in statistics.If a business student is selected at random and found to be enrolled in statistics, what is the probability that the student is also enrolled in accounting?

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?

Which of the following statements concerning the F distribution is true?

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

Disco Fever is randomly found in one half of one percent of the general population.Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease.The test also yields a false-positive in 4% of the cases where the disease is not present.What is the probability that the disease is not present if the test result is positive?