Exam 6: Discrete Probability Distributions

A manufacturer receives a shipment of 170 laptop computers of which 11 are defective. To test the shipment,the quality control engineer randomly selects 20 computers from the shipment and tests them. The randomvariable X represents the number of defective computers in the sample. What is the probability of obtaining 3defective computers?

A hypergeometric probability experiment is conducted with the given parameters. Compute the probability ofobtaining x successes. $\mathrm { N } = 130 , \mathrm { n } = 10 , \mathrm { k } = 25 , \mathrm { x } = 3$

A small life insurance company has determined that on the average it receives 3 death claims per day. Find theprobability that the company receives at least seven death claims on a randomly selected day.

The university police department keeps track of the number of tickets it write in a year. Last year the campuspolice wrote 1460 tickets. Ticket writing on campus follows a Poisson process. What is the standard deviationof the number of tickets written per day by the campus police?

Classify the following random variable according to whether it is discrete or continuous. -the age of the oldest dog in a kennel

Draw the probability histogram and label the mean for n = 8 and p = 0.3

A university must choose a team of 6 students to participate in a TV quiz show. The students will be chosenfrom a pool of 32 potential participants of whom 14 are women. If the 6 students are chosen at random, what isthe probability that the team will contain 2 women?

Mamma Temte bakes six pies a day that cost $2 each to produce. On 15% of the days she sells only two pies. On30% of the days, she sells 4 pies, and on the remaining 55% of the days, she sells all six pies. If Mama Temtesells her pies for $6 each, what is her expected profit for a dayʹs worth of pies? [Assume that any leftover piesare given away.]

True or False: The expected value of a discrete probability distribution may be negative.

A jury is to be selected from a pool of 34 potential jurors. The defendant faces the death penalty if convicted. Ofthe potential jurors, 7 are opposed to the death penalty. The jury consists of 12 randomly selected jurors. Therandom variable X represents the number of jurors who oppose the death penalty.

A lab orders a shipment of 100 rats a week, 52 weeks a year, from a rat supplier for experiments that the labconducts. Prices for each weekly shipment of rats follow the distribution below: Price \ 10.00 \ 12.50 \ 15.00 Probability 0.2 0.3 0.5 How much should the lab budget for next yearʹs rat orders assuming this distribution does not change. (Hint:find the expected price.)

On one busy holiday weekend, a national airline has many requests for standby flights at half of the usualone-way air fare. However, past experience has shown that these passengers have only about a 1 in 5 chance ofgetting on the standby flight. When they fail to get on a flight as a standby, their only other choice is to fly firstclass on the next flight out. Suppose that the usual one-way air fare to a certain city is $142 and the cost offlying first class is $395. Should a passenger who wishes to fly to this city opt to fly as a standby? [Hint: Findthe expected cost of the trip for a person flying standby.]

Consider the discrete probability distribution to the right when answering the following question. Find theprobability that x equals 5. 2 5 6 8 () 0.16 ? 0.3 0.21

Classify the following random variable according to whether it is discrete or continuous. -the number of emails received on any given day

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poissondistribution with a mean of 6.3. Find the probability that the next two months will both result in five accidentseach occurring on this stretch of road.

An online retailer receives an average of five orders per 500 hits on its website. If it gets 100 hits on its website,find the probability of receiving at least two orders. Use the Poisson distribution.

A recent article in the paper claims that government ethics are at an all-time low. Reporting on a recent sample,the paper claims that 45% of all constituents believe their representative possesses low ethical standards.Suppose 20 of a representativeʹs constituents are randomly and independently sampled. Assuming the paperʹsclaim is correct, find the probability that more than eight but fewer than 12 of the 20 constituents sampledbelieve their representative possesses low ethical standards.

Classify the following random variable according to whether it is discrete or continuous. -the temperature in degrees Celsius on January 1st in Fargo, North Dakota

According to government data, the probability that an adult was never in a museum is 15%. In a randomsurvey of 10 adults, what is the probability that two or fewer were never in a museum?

In the American version of the Game Roulette, a wheel has 18 black slots, 8 red slots and 2 green slots. All slotsare the same size. In a carnival game, a person wagers $2 on the roll of two dice. A person can wager on eitherred or black. Green is reserved for the house. If a player wagers $5 on either red or black and that color comesup, they win $10 otherwise they lose their wager. What is the expected value of playing the game once?