Exam 5: Discrete Distributions

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 3 cars arriving over a five-minute interval is _______.

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business,but after scanning the list she doubts the authenticity of the list.She randomly selects five names from the list for validation.If 40% of the names on the list are non-authentic,and x is the number of non-authentic names in her sample,P(x=0)is ______________.

The following graph is a binomial distribution with n = 6. This graph reveals that ____________.

Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 men and 5 women.The probability that all three faculty selected are men is approximately _______

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

In a certain communications system,there is an average of 1 transmission error per 10 seconds.Assume that the distribution of transmission errors is Poisson.The probability of 1 error in a period of one-half minute is approximately ________

For a binomial distribution in which the probability of success is p = 0.5,the variance is twice the mean.

The following graph is a binomial distribution with n = 6. This graph reveals that ____________.

For the Poisson distribution the mean represents twice the value of the standard deviation..

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 1,2006.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 _______________.

To compute the variance of a discrete distribution,it is not necessary to know the mean of the distribution.

Assume that a random variable has a Poisson distribution with a mean of 5 occurrences per ten minutes.The number of occurrences per hour follows a Poisson distribution with λ equal to _________

A binomial distribution is better than a Poisson distribution to describe the occurrence of major oil spills in the Gulf of Mexico.

A large industrial firm allows a discount on any invoice that is paid within 30 days.Of all invoices,10% receive the discount.In a company audit,15 invoices are sampled at random.The mean (average)value of the number of the 15 sampled invoices that receive discount is _______

A market research team compiled the following discrete probability distribution on the number of sodas the average adult drinks each day.In this distribution,x represents the number of sodas which an adult drinks. The mean (average)value of x is _______________.

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 batch contains two defective boards; and x is the number of defective boards in the sample.P(x=1)is _______.

The number of bags arriving on the baggage claim conveyor belt in a 3 minute time period would best be modeled with the _________.

The speed at which a jet plane can fly is an example of _________.

On Monday mornings,customers arrive at the coffee shop drive thru at the rate of 6 cars per fifteen minute interval.Using the Poisson distribution,the probability that five cars will arrive during the next five minute interval is _____________.

The assumption of independent trials in a binomial distribution is not a great concern if the sample size is smaller than 1/20^th of the population size.