Exam 6: Discrete Probability Distributions

Determine Whether a Probability Experiment is a Hypergeometric Experiment -A jury is to be selected from a pool of 38 potential jurors. The defendant faces the death penalty if convicted. Of the potential jurors, 7 are opposed to the death penalty. The jury consists of 12 randomly selected jurors. The random variable $X$ represents the number of jurors who oppose the death penalty.

Compute Probabilities of a Poisson Random Variable -The number of goals scored at State College hockey games follows a Poisson distribution with a mean of 4 goals per game. Find the probability that each of three randomly selected State College hockey games resulted in five goals being scored.

Classify the following random variable according to whether it is discrete or continuous -the number of bottles of juice sold in a cafeteria during lunch

Compute the Variance and Standard Deviation of a Discrete Random Variable -In a sandwich shop, the following probability distribution was obtained. The random variable $x$ represents the number of condiments used for a hamburger. Find the mean and standard deviation for the random variable x. x P(x) 0 0.30 1 0.40 2 0.20 3 0.06 4 0.04

Compute the Mean and Standard Deviation of a Binomial Random Variable -According to insurance records, a car with a certain protection system will be recovered 94% of the time. If 300 stolen cars are randomly selected, what is the mean and standard deviation of the number of cars recovered after being stolen

Classify the following random variable according to whether it is discrete or continuous -The peak shopping time at home improvement store is between 8:00am-11:00 am on Saturday mornings. Management at the home improvement store randomly selected 190 customers last Saturday morning and decided to observe their shopping habits. They recorded the number of items that each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the home improvement store.

Compute the Probabilities of Hypergeometric Experiments -A hypergeometric probability experiment is conducted with the given parameters. Compute the probability of obtaining $x$ successes. $\mathrm { N } = 120 , \mathrm { n } = 15 , \mathrm { k } = 30 , \mathrm { x } = 2$

Construct Binomial Probability Histograms -Draw the probability histogram and label the mean for n = 8 and p = 0.3

Compute Probabilities of a Poisson Random Variable -Suppose x is a random variable for which a Poisson probability distribution with = 5.3 provides a good characterization. Find for x.

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

Determine Whether a Probability Experiment is a Binomial Experiment -Decide whether the experiment is a binomial experiment. If it is not, explain why. Each week, a man attends a club meeting in which he has a 36% chance of meeting a new member. The random variable is the number of times he meets a new member in 92 weeks.

Compute Probabilities of a Poisson Random Variable -The local police department receives an average of two calls per hour. Use the Poisson distribution to determine the probability that in a randomly selected hour the number of calls is five.

Determine Whether a Probability Experiment is a Binomial Experiment -Decide whether the experiment is a binomial experiment. If it is not, explain why. Survey 150 college students see whether they are enrolled as a new student. The random variable represents the number of students enrolled as new students.

Compute the Probabilities of Hypergeometric Experiments -A manufacturer receives a shipment of 160 laptop computers of which 12 are defective. To test the shipment, the quality control engineer randomly selects 25 computers from the shipment and tests them. The random variable X represents the number of defective computers in the sample. What is the probability of obtaining 4 defective computers

Construct Probability Histograms -A baseball player is asked to swing at pitches in sets of four. The player swings at 100 sets of 4 pitches. The probability distribution for making a particular number of hits is given below. Determine the mean for this discrete probability distribution. x 0 1 2 3 4 P(x) 0.02 0.07 0.22 0.27 0.42

Determine Whether a Probability Experiment is a Hypergeometric Experiment -Of the 3800 students at a college, 280 are mature students. 50 students are selected at random from the 3800 students at the college and asked to participate in a survey. The questions in the survey relate to the student's need for financial assistance. The random variable $X$ represents the number of mature students in the sample.

Interpret the Mean of a Discrete Random Variable as an Expected Value -On one busy holiday weekend, a national airline has many requests for standby flights at half of the usual one-way air fare. However, past experience has shown that these passengers have only about a 1 in 5 chance of getting on the standby flight. When they fail to get on a flight as a standby, their only other choice is to fly first class on the next flight out. Suppose that the usual one-way air fare to a certain city is $194 and the cost of flying first class is $520. Should a passenger who wishes to fly to this city opt to fly as a standby [Hint: Find the expected cost of the trip for a person flying standby.]

Construct Probability Histograms -Use the frequency distribution to (a) construct a probability distribution for the random variable $x$ which represents the number of cars per family in a town of 1000 families, and (b) graph the probability histogram. Cars Families 0 125 1 428 2 256 3 108 4 83

Compute Probabilities of Binomial Experiments -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 42% of all constituents believe their representative possesses low ethical standards. Assume that responses were randomly and independently collected. A representative of a district with 1,000 people does not believe the paper s claim applies to her. If the claim is true, how many of the representative s constituents believe the 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