Exam 6: Discrete Probability Distributions

In response to a major competitor,a local pizza company begins to pay $5 to customers whose home delivered pizza did not arrive within 30 minutes after the order was placed.Explain why you applied that specific distribution to answer the preceding question.

A cashier at Carter's cafeteria can total an average of 2.2 trays per minute. -A cashier at Carter's cafeteria can total an average of 2.2 trays per minute.The probability that the cashier will total between four and ten trays in a minute is:

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 at least 4 calls in an hour is:

Chamber of Commerce A local chamber of commerce is backing a plan for a new convention center.The chamber states that 60 percent of the voters favor the plan,which would raise tourism business and taxes for the residents.Four of the registered voters in the community are called at random.X is the number of voters called who say they favor the plan. -Find the probability that exactly 2 voters sampled favor the plan.

Brendalee and Mohammed go to a coffee shop during their lunch break and toss a coin to see who will pay.The probability that Brendalee will pay three days in a row is:

The ____________________ probability distribution deals with consecutive trials with only two outcomes that are not statistically independent.

Canoe club A canoe club sponsor has taken canoeing groups through a particularly rough section of white water on a mountain river.Past trips and experience of the sponsor lead her to believe that fifty percent of the canoeists who attempt to paddle their way through this section will overturn.At the present time,there are five canoes approaching this treacherous section.Assume that the sponsor's estimate of the probability of a canoe overturning in this section of water is accurate. -What is the probability that none of the five canoes will capsize?

Canoe club A canoe club sponsor has taken canoeing groups through a particularly rough section of white water on a mountain river.Past trips and experience of the sponsor lead her to believe that fifty percent of the canoeists who attempt to paddle their way through this section will overturn.At the present time,there are five canoes approaching this treacherous section.Assume that the sponsor's estimate of the probability of a canoe overturning in this section of water is accurate. -What is the probability that two of the five canoes will capsize?

Chocolates A box of chocolates contains 18 pieces,10 of which have nuts while the remaining 8 do not.Four pieces are chosen at random. -What is the probability that at least 3 pieces have nuts?

The binomial distribution is best used to describe the number of customers arriving at a service point during a given period of time.

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 more than five sheets are sub-standard?

MBI Co. The MBI Company found that at the end of each month,2% of its two million accounting entries contained errors.Today,one operator has made 50 computer entries. What is the probability that at most two errors were made?

Chocolates A box of chocolates contains 18 pieces,10 of which have nuts while the remaining 8 do not.Four pieces are chosen at random. -What is the probability that no more than one piece has nuts?

Compute the following probabilities (to 4 decimal places)using the Poisson formula: A)P(x = 3),if $\lambda$ = 2.5 B)P(x ≤ 1),if $\lambda$ = 2.0 C)P(x ≥ 2),if $\lambda$ = 3.0

Canoe club A canoe club sponsor has taken canoeing groups through a particularly rough section of white water on a mountain river.Past trips and experience of the sponsor lead her to believe that fifty percent of the canoeists who attempt to paddle their way through this section will overturn.At the present time,there are five canoes approaching this treacherous section.Assume that the sponsor's estimate of the probability of a canoe overturning in this section of water is accurate. -What is the probability that only one of the five canoes will capsize?

List the four characteristics of a Bernoulli process.

Stabbings of inmates by other inmates at a state prison unit have averaged 2.6 per month over the past year.Let x be the number of inmate stabbings per month.Assume a Poisson distribution.Find the mean and standard deviation of x. Mean = ____________________ SD = ____________________

Students Students use the university mainframe computer log-on during their designated time periods.Assume that the number of students logging on each five-minute interval is 12.5,and these log-on attempts are Poisson distributed. -Find the probability that more than 6 students will log-in during the next 5-minute interval.

Fishing During the peak fishing months,a marina at a large man-made reservoir noted that boats were arriving at the average of 3.2 boats every twenty minutes to use the boat ramp.Let x be the number of boats arriving during the next twenty minutes. -What is the probability that during the next twenty minutes the number of boats arriving to load or unload is exactly three?

The expected value,E(x),of a binomial probability distribution is: