Exam 2: Probability Concepts and Applications

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?

A consulting firm has received 2 Super Bowl playoff tickets from one of its clients. To be fair, the firm is randomly selecting two different employee names to "win" the tickets. There are 6 secretaries, 5 consultants, and 4 partners in the firm. Which of the following statements is true?

Which distribution is helpful in testing hypotheses about variances?

The standard deviation equals the square of the variance.

"The probability of event B, given that event A has occurred" is known as a ________ probability.

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 more than 40 minutes?

A dry cleaning business offers a pick-up and delivery service for a 10 percent surcharge. Management believes 60 percent of customers will take advantage of this service. They are also considering offering customers the option of opening an account and receiving monthly bills. They believe 60 percent of their customers (regardless of whether or not they use the pick-up service) will use the account service. If the two services are introduced to the market, what is the probability a customer uses both services?

A consulting firm has received 2 Super Bowl playoff tickets from one of its clients. To be fair, the firm is randomly selecting two different employee names to "win" the tickets. There are 6 secretaries, 5 consultants and 4 partners in the firm. Which of the following statements is not true?

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 product will be successful if the market research indicates a failure?

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: (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?

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, (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"?

In a normal distribution the Z value represents the number of standard deviations from a value X to the mean.

If we roll a single die twice, the probability that the sum of the dots showing on the two rolls equals four (4), is 1/6.

The equation P(A|B) = P(AB)/P(B) is

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 enrolled in both statistics and accounting?

A company is considering producing two new electronic games designed for the popular Gameboy toy. Based on market data, management believes there is a 60 percent chance that a "cops and robbers" game will be successful and a 40 percent chance that a "let's play house" game will be successful. As these products are completely different, it may be assumed that the success of one is totally independent of the success of the other. If two products are introduced to the market, what is the probability that both are successful?

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

What is the F value associated with α = 0.05, numerator degrees of freedom (df₁) equal to 4, and denominator degrees of freedom (df₂) equal to 9?

Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers per hour. What is the probability that in the next hour there will be exactly 8 arrivals?

Suppose that, historically, April has experienced rain and a temperature between 35 and 50 degrees on 20 days. Also, historically, the month of April has had a temperature between 35 and 50 degrees on 25 days. You have scheduled a golf tournament for April 12. If the temperature is between 35 and 50 degrees on that day, what will be the probability that the players will get wet?