Exam 5: Discrete Random Variables

During off hours,cars arrive at a tollbooth on the East-West toll road at an average rate of 0.5 cars per minute.The arrivals are distributed according to a Poisson distribution.What is the probability that during the next minute,three cars will arrive?

If p = .5 and n = 4,then the corresponding binomial distribution is ____________.

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10 percent.If 10 calculators are selected at random,what is the probability that 3 or more of the calculators will be defective?

Which of the following is a valid probability value for a discrete random variable?

Suppose that x has a hypergeometric distribution with N = 10,r = 5,and n = 3.Calculate the standard deviation of the distribution.

If x is a binomial random variable,then the standard deviation of x is given by:

A large disaster cleaning company estimates that 30 percent of the jobs it bids on are finished within the bid time.Looking at a random sample of 8 jobs that it has contracted,find the probability that x (number of jobs finished on time)is within one standard deviation of the mean.

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.If X = the number of arrivals per minute,find the probability of 10 customers or fewer arriving within a minute.

An insurance company will insure a $75,000 Hummer for its full value against theft at a premium of $1500 per year.Suppose that the probability that the Hummer will be stolen is 0.0075.Find the premium that the insurance company should charge if it wants its expected net profit to be $2000.

Twenty coins are tossed.What is the probability of getting exactly 10 heads?

If the number of surface nonconformities on a specific size of a metal piece is the discrete random variable in question,then the appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 nonconformities is most likely given by the binomial distribution.

An appliance manufacturer gives a warranty,and 95 percent of its appliances do not require repair before the warranty expires.An organization buys 10 of these appliances.Calculate an interval that contains 95.44 percent of all the appliances that will not require repair.

Suppose you randomly select 3 DVDs from a production run of 10.Of the 10 DVDs,9 are expected to last a minimum of 3 years.What is the mean of the random variable x?

The manager of the local grocery store has determined that,on average,4 customers use the service desk every half-hour.Assume that the number of customers using the service desk has a Poisson distribution.What is the probability that during a randomly selected half-hour period,no more than 2 customers use the service desk?

Historical data for a local steel manufacturing company show that the average number of defects per standard sheet of steel is 2.In addition,the number of defects per unit is distributed according to a Poisson distribution.What is the probability that there will be a total of 7 defects on four standard sheets of steel?

A multiple-choice test has 30 questions and each one has five possible answers,of which one is correct.If all answers were guesses,find the probability of getting exactly four correct answers.

An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired.Historically,the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day.For the first five troubles reported on a given day,find the mean number of troubles repaired on the same day.

Historical data show that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every two hours.Assume that the patient arrivals are distributed according to a Poisson distribution.Determine the probability of 6 patients arriving in a five-hour period.

The Securities and Exchange Commission has determined that the number of companies listed on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month.Find the probability that exactly 4 bankruptcies occur next month.

In a binomial distribution,the random variable X is continuous.