Exam 2: Probability Concepts and Applications

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 is negative?

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.What is the probability that a student uses more than 350 minutes?

Explain why event probabilities range from 0 to 1.

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

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 less than 3 minutes for a particular customer to get a license renewal?

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.What is the probability that a student uses between 400 and 500 minutes?

Drivers arrive at a toll booth at a rate of 3 per minute during peak traffic periods.The time between consecutive driver arrivals follows an exponential distribution.What is the probability that it will take less than 1/2 of a minute between consecutive drivers?

Drivers arrive at a toll booth at a rate of 3 per minute during peak traffic periods.The time between consecutive driver arrivals follows an exponential distribution.What is the probability that it will take more than 1/3 of a minute between consecutive drivers?

The number of phone calls coming into a switchboard in the next five minutes will either be 0, 1, or 2.The probabilities are the same for each of these (1/3).If X is the number of calls arriving in a five-minute time period, what is the mean of X?

Assume that you have a box containing five balls: two red and three white.You draw a ball two times, each time replacing the ball just drawn before drawing the next.The probability of drawing only one white ball is 0.20.

A dry cleaning business offers a pick-up and delivery service for a 10 percent surcharge.Management believes 60 percent of the existing 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 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 that a customer uses only one of these services?

Customer arrivals occur at a rate of 1.2 per minute.The time between customer arrivals follows an exponential distribution.What is the probability that it takes between 1 and 2 minutes between customer arrivals?

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 company is considering producing two new electronic games designed for the popular Gameboy toy.Based on market data, management believes that 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?

For df₁ = 3 and df₂ = 7, what is the probability that F is greater than 5?

Michael's arms windmilled, propelling him through the water at a pace few could believe.He completed his 100 meter butterfly in 49.82 seconds and was pleased with his performance.At the ceremony later that afternoon, Michael and the other seven finalists were awarded participation medals, which he found distressing.He was quick to point out that the average time for the 100 meter butterfly was 53 seconds with a standard deviation of 0.9 seconds.There must be some way of demonstrating how exceptional his time was, so he turned to his friend who was studying quantitative analysis to help him prove this.How exceptional is Michael's performance?

Which of these suggests a continuous random variable?

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?

The expected value of a probability distribution is

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?