Exam 6: Discrete Probability Distributions

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 nine calls in an hour is:

Daisy wheel A manufacturer of daisy wheel print heads for typewriters and printers knows that 1.5% of the print heads manufactured have a defect.If a production run is 120 print heads. -Determine the probability that at most one is defective.

A high school play has five roles to fill with students.Seven girls and nine boys have expressed an interest in the play.What is the probability that exactly 0 girls will be selected?

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 no more than three trays in a minute is:

The Poisson distribution is applied to events for which the probability of occurrence over a given span of time,space,or distance is ____________________.

A characteristic of a Bernoulli process is that the trials are statistically dependent; that is,the outcome in any trial is affected by the outcomes of earlier trials,and it does affect the outcomes of later trials.

Approximately 84% of persons age 70 to 84 live in their own household and are income-qualified for home purchases.If four persons are randomly selected from this population,the probability that exactly two of the four live in their own household and are income-qualified is:

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. -What is the probability that at least one T.V.home in the sample is served by cable?

The driving time between Big Rapids and Grand Rapids is an example of a discrete random variable.

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 from two to four?

Game show A game show contestant is shown 20 suitcases,3 of which have a prize inside.They have 3 opportunities to choose a suitcase. -What is the probability that at least two of these suitcases has a prize?

Stockholders The listed occupations of stockholders of a regional electric utility company included 9 percent who were homemakers.Six of these stockholders are randomly selected. -What is the probability that exactly three are homemakers?

In general,we can define a ____________________ as the relative frequency distribution that should theoretically occur for observations from a given population.

Game show A game show contestant is shown 20 suitcases,3 of which have a prize inside.They have 3 opportunities to choose a suitcase. -What is the probability that none of these suitcases has a prize?

Assume that you used Minitab statistical package to generate the individual binomial probabilities when n = 100 and $\pi$ = .042,and then generate the individual Poisson probabilities for $\lambda$ = 4.2.Do you expect the probabilities obtained in both cases to be similar or different? Explain.

Which of the following is a discrete random variable?

What is the standard deviation of the number of canoes that will capsize?

An advertising executive receives an average of 10 telephone calls each afternoon between 2 and 4 pm.The calls occur randomly and independently of one another. A)Find the probability that the executive will receive 12 calls between 2 and 4 pm on a particular afternoon. B)Find the probability that the executive will receive eight calls between 2 and 3 pm on a particular afternoon. C)Find the probability that the executive will receive at least six calls between 2 and 4 pm on a particular afternoon.

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 -What is the probability that a randomly selected Egyptian household will have between 2 and 4 children?

Tornadoes for January in Kansas average 3.2 per month.The probability that in the next January at least 2 tornadoes will occur is: