Exam 5: Several Useful Discrete Distributions

It has been alleged that 40% of all community college students favour Dell computers. If this were true, and we took a random sample of 25 students, the binomial probability table for cumulative values of x available in your text would reveal which of the following probabilities?

The Poisson probability distribution provides a good approximation to binomial probabilities when n is large and = np is small, preferably with np < 7.

Warehouse Narrative A warehouse contains ten computer printers, four of which are defective. A company randomly selects five of the ten printers to purchase. -Refer to Warehouse Narrative. What is the mean of x?

Which of the following best describes a binominal probability distribution?

A manufacturer of golf balls uses a production process that produces 10% defective balls. A quality inspector takes samples of a week's output with replacement. Using the cumulative binomial probability table available in your text, which of the following probabilities can the inspector determine?

The number of traffic accidents per day on a certain section of highway is thought to be distributed with a mean equal to 2.19. What is the standard deviation of the number of accidents?

Bicycle Repair Shop Narrative The number of people arriving at a bicycle repair shop follows a Poisson distribution, with an average of five arrivals per hour. Let x represent number of people arriving per hour. -Refer to Bicycle Repair Shop Narrative. What is the probability that seven people arrive at the bike repair shop in a one-hour period?

The mean of a Poisson distribution variable, where is the average number of successes occurring in a specified interval, is .

Which probability distribution is appropriate when the events of interest occur randomly, independently of one another, and rarely?

Which of the following is NOT a characteristic of a binomial ?

Computer Disks Narrative The quality of computer disks is measured by sending the disks through a certifier that counts the number of missing pulses. A certain brand of computer disks averages 0.1 missing pulses per disk. Let the random variable x denote the number of missing pulses. -Refer to Computer Disks Narrative. Find the probability neither of the next two disks inspected will contain any missing pulse.

Automobile Spark Plugs Narrative An eight-cylinder automobile engine has two misfiring spark plugs. The mechanic removes all four plugs from one side of the engine. -Refer to Automobile Spark Plugs Narrative. What is the mean number of misfiring spark plugs?

Which of the following is NOT a characteristic of a binomial experiment?

Bicycle Repair Shop Narrative The number of people arriving at a bicycle repair shop follows a Poisson distribution, with an average of five arrivals per hour. Let x represent number of people arriving per hour. -Refer to Bicycle Repair Shop Narrative. What is the probability that, at most, seven people arrive at the bike repair shop in a one-hour period?

Defective Items Narrative A random sample of 4 units is taken from a group of 15 items in which 4 units are known to be defective. Assume that sampling occurs without replacement, and the random variable x represents the number of defective units found in the sample. -Refer to Defective Items Narrative. Evaluate P(x = 4).

Insulin-Dependent Diabetes Narrative Insulin-dependent diabetes (IDD) is a common chronic disorder of children. Let us assume that an area in Europe has an incidence of 6 cases per 100,000 per year. -Refer to Insulin-Dependent Diabetes Narrative. Can the distribution of the number of cases of IDD in this area be approximated by a Poisson distribution? If so, what is the mean? Justify your answers.

Suppose we are given that n is the number of trials of a random experiment, N is population size, M is the number of population units with the "success" characteristic, and p is the probability of success in the first trial. Under those circumstances, which of these expressions equals the mean of the hypergeometric random variable's probability distribution?

Defective Items Narrative A random sample of 4 units is taken from a group of 15 items in which 4 units are known to be defective. Assume that sampling occurs without replacement, and the random variable x represents the number of defective units found in the sample. -Refer to Defective Items Narrative. What is the variance of the random variable x?

A shipment of six parrots from Brazil includes two parrots with a potentially fatal disease. As usual, the Customs Office at the shipment's point of entry randomly samples two parrots and tests them for disease. Let the random variable x be the number of healthy parrots in the sample. Find the probability distribution of x.

Toll Station Narrative It is known that between 8 and 10 a.m. on Saturdays, cars arrive at a certain toll station at a rate of 60 per hour. Assume that a Poisson process is occurring and that the random variable x represents the number of cars arriving at the station between 9:00 and 9:05 a.m. -Refer to Toll Station Narrative. Find P(x = 5).