Exam 6: Discrete Probability Distributions

Poisson Distribution One half of one percent of the checks received by an oil company are returned due to insufficient funds.Yesterday 500 checks were received in the mail.Let x equal the number of these checks which will be returned due to insufficient funds. -Use the Poisson distribution to compute the binomial probability that less than three checks are returned.

Motor Co. A Motor Company has purchased steel parts from a supplier for several years and has found that 10% of the parts must be returned because they are defective.An order of 25 parts is received. What are the mean and standard deviation of the defective parts? Mean = ____________________ SD = ____________________

The probability of success in a hypergeometric distribution does not remain constant from one trial to another.

Tornadoes for January in Kansas average 3.2 per month.The probability that in the next January there will be between 1 and 3 tornadoes (inclusive)is:

Egyptian Let x represent the number of children in an Egyptian household.The probability distribution of x is as follows: x 1 2 3 4 5 p(x) 0.25 0.33 0.17 0.15 0.10 -Find the expected number of children in a randomly selected Egyptian household.

A machine wraps and twists the ends of a wrapper for peppermint candy at a rate of 100 per minute.However,the machine malfunctions on the average of 1 per minute.Assume that the malfunctions are a Poisson distribution and let x denote the number of candies which are not wrapped due to the malfunction.What is the probability that between zero and four candies will be unwrapped in a given minute?

The number of life insurance policy holders is an example of a discrete random variable.

Plywood Manufacturer A plywood manufacturer produces an exterior grade of plywood for which 0.3 percent fails to meet the industry standard.One thousand sheets are purchased by a lumberyard for retail sale.Use the Poisson distribution to approximate the binomial distribution. -What is the probability that none of the sheets sold are sub-standard?

Which of the following most likely represents a discrete random variable?

The likelihood that someone who logs onto a particular site in a "shopping mall" on the Internet will purchase an item is 0.05 and follows the binomial distribution.If the site has 35 people accessing it in the next hour,what is the expected number of successes during this hour?

Police A local police station receives an average 8.1 emergency telephone calls per hour.These calls are Poisson distributed. -The probability that the station will get five to seven calls in an hour is:

A recent survey in Michigan revealed that 60% of the vehicles traveling on highways,where speed limits are posted at 70 miles per hour,were exceeding the limit.Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour.Let x denote the number vehicles that were exceeding the limit.Find the following probabilities: a.P(x = 10) b.P(4 < x < 9) c.P(3 $\le$ x $\le$ 10

New York City New York City is estimated to have 21 percent of the homes with T.V.sets served by cable T.V.If a random sample of four is taken from these homes find the probability distribution of x where x is the number of T.V.homes in the sample having cable T.V. Compute the mean and standard deviation of the number of T.V.homes with cable service in the sample. Mean = ____________________ Standard deviation = ____________________

Appliance store A small appliance store has 10 VCR's in stock.Four of the VCR's were damaged in shipment.The owner of the store gives his daughter and his son each a VCR for a birthday present. What is the probability that both the gift VCR's will be defective?

A barbershop requires appointments for perms and hair cuts.Ten percent of those making appointments cancel or simply fail to show up.Next week's appointment calendar has 64 appointments.Let x be the number of missed appointments out of the 64.The probability that more than 3 cancellations and/or no-shows will occur during the next week is:

Plywood Manufacturer A plywood manufacturer produces an exterior grade of plywood for which 0.3 percent fails to meet the industry standard.One thousand sheets are purchased by a lumberyard for retail sale.Use the Poisson distribution to approximate the binomial distribution. -What is the probability that fewer than three sheets are sub-standard?

A random variable that can take on only certain values along an interval,with the possible values having gaps between them,is referred to as a ____________________.

The binomial distribution samples ____________________ replacement while the hypergeometric distribution samples ____________________ replacement.

For a Bernoulli process in which the number of trials is large and the probability of success on any given trial is very small,the Poisson distribution can be used as an approximation to the binomial distribution.

Theoretically,the number of successes in a binomial distribution has no limit.