Exam 5: Discrete Distributions

The mean or the expected value of a discrete distribution is the long-run average of the occurrences.

For the Poisson distribution,the mean and the variance are the same.

A variable that can take on values at any point over a given interval is called a discrete random variable.

Aluminum castings are processed in lots of five each.A sample of two castings is randomly selected from each lot for inspection.A particular lot contains one defective casting;and x is the number of defective castings in the sample.P(x=1)is ___.

Suppose a committee of 3 people is to be selected from a group consisting of 4 men and 5 women.What is the probability that all three people selected are men?

Circuit boards for wireless telephones are etched in an acid bath,in batches of 100 boards.A sample of seven boards is randomly selected from each lot for inspection.A particular batch contains two defective boards;and x is the number of defective boards in the sample.P(x=2)is ___.

The Poisson distribution is a discrete distribution.

In a binomial distribution,p,the probability of getting a successful outcome on any single trial,remains the same from one trial to another.

You are offered an investment opportunity.Its outcomes and probabilities are presented in the following table: The standard deviation of this distribution is ___.

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc. ,suspects irregularities in the payroll system,and orders an inspection of a random sample of vouchers issued since January 1,2013.A sample of ten vouchers is randomly selected,without replacement,from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contain errors,P(x>0)is ___.

One hundred policyholders file claims with CareFree Insurance.Ten of these claims are fraudulent.Claims manager Earl Evans randomly selects four of the ten claims for thorough investigation.If x represents the number of fraudulent claims in Earl's sample,x has a ___.

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc. ,suspects irregularities in the payroll system,and orders an inspection of a random sample of vouchers issued since January 1,2013.A sample of ten vouchers is randomly selected,without replacement,from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contain errors,P(x = 0)is ___.

The volume of liquid in an unopened 1-litre can of paint is an example of ___.

On Saturdays,cars arrive at Sam Schmitt's Scrub and Shine Car Wash at the rate of 6 cars per fifteen-minute interval.Using the Poisson distribution,the probability that five cars will arrive during the next fifteen-minute interval is ___.

You are offered an investment opportunity.Its outcomes and probabilities are presented in the following table: Which of the following statements is true?

Twenty five items are sampled.Each of these has the same probability of being defective.The probability that exactly 2 of the 25 are defective could best be found by ___.

If x is the number of successes in an independent series of 10 trials,then x has a ___ distribution.

The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals.The probability of 5 cars arriving over a five-minute interval is ___.

As in a binomial distribution,each trial of a hypergeometric distribution results in one of two mutually exclusive outcomes,i.e. ,either a success or a failure.

A market research team compiled the following discrete probability distribution for families residing in Randolph County.In this distribution x represents the number of evenings the family dines outside their home during a week. The standard deviation of x is ___.