Exam 5: Several Useful Discrete Distributions

Where n = 150 is the number of trials and p = 0.6 is the probability of success in each trial, the standard deviation of a binomial experiment is 36.

A warehouse contains six parts made by company A and ten parts made by company B. If four parts are selected at random from the warehouse, the probability that none of the four parts is from company A is approximately 0.1154.

What does the binomial distribution formula do?

For a binomial experiment with n trials, p is the probability of success, q is the probability of failure, and x is the number of successes in n trials. Which one of the following statements is NOT a property of such an experiment?

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 probability the two misfiring spark plugs are among those removed?

Automobile Service Centre Narrative An automobile service centre can take care of eight cars per hour. Assume that the cars arrive at the service centre randomly and independently of each other at a rate of six per hour, on average. -Refer to Automobile Service Centre Narrative. What is the probability that fewer than two cars will be in the service centre at any point during a given hour?

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. What is the standard deviation of the number of cars arriving at the toll station between 9:00 and 9:05 a.m.?

The number of teleport inquiries, x, in a timesharing computer system averages 0.2 per millisecond and follows a Poisson distribution. a. Find the probability that no inquiries are made during the next millisecond. b. Find the probability that no inquiries are made during the next three milliseconds.

It is known that in an Introductory Statistics class of 20 students, 70% of them own smartphones. If you were to randomly pick 10 students from that class, what is the probability that 70% of those picked would have smartphones?

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 variance of x?

Which of the following distributions could NOT be used to describe the exact distribution for a discrete random variable?

Given a Poisson random variable x, where the average number of times an event occurs in a certain period of time or space is 1.5, then what is P(x = 2)?

Which of the following experiments CANNOT be modelled by a Poisson distribution?

Automobile Service Centre Narrative An automobile service centre can take care of eight cars per hour. Assume that the cars arrive at the service centre randomly and independently of each other at a rate of six per hour, on average. -Refer to Automobile Service Centre Narrative. What is the probability that exactly six cars will be in the service centre at any point during a given hour?

A warehouse contains six parts made by company A and ten parts made by company B. If four parts are selected at random from the warehouse, the probability that all four parts are from company B is approximately 0.008.

Let x be a binomial random variable with n = 20 and p = 0.05. a. Calculate using the cumulative binomial probabilities table in Appendix I of your text. b. Use the Poisson approximation to calculate c. Compare the results of (a) and (b). Is the approximation accurate?

When sampling without replacement, which of the following is the appropriate probability distribution to use?

What kinds of probabilities does the hypergeometric probability distribution provide?

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 between four and nine people, inclusively, arrive at the bike repair shop in a one-hour period?

Scholarship Narrative A college has seven applicants for three scholarships: four females and three males. Suppose the seven applicants are equally qualified and no preference is given by the selection committee for choosing either gender. Let x equal the number of female students chosen for the three scholarships. -Refer to Scholarship Narrative. What is the mean of the distribution of x?