Exam 6: Discrete Probability Distributions

Suppose the number of babies born during an 8-hour shift at a hospitalʹs maternity wing follows a Poissondistribution with a mean of 5 an hour. Find the probability that three babies are born during a particular1-hour period in this maternity wing.

The probability that an individual has 20-20 vision is 0.17. In a class of 68 students, what is the probability offinding five people with 20-20 vision?

The random variable x represents the number of girls in a family of three children. Assuming that boys andgirls are equally likely, find the mean and standard deviation for the random variable x.

The produce manager at a farmerʹs market was interested in determining how many oranges a person buyswhen they buy oranges. He asked the cashiers over a weekend to count how many oranges a person boughtwhen they bought oranges and record this number for analysis at a later time. The data is given below in thetable. The random variable x represents the number of oranges purchased and P(x) represents the probabilitythat a customer will buy x apples. Determine the mean number of oranges purchased by a customer. x 1 2 3 4 5 6 7 8 9 10 P(x) 0.05 0.19 0.20 0.25 0.12 0.10 0 0.08 0 0.01

According to insurance records a car with a certain protection system will be recovered 87% of the time. Findthe probability that 4 of 10 stolen cars will be recovered.

Provide an appropriate response. -The random variable x represents the number of tests that a pet entering an animal shelter will have along withthe corresponding probabilities. Graph the probability histogram. x P(x) 0 1 2 3 4

Given that a random variable x, the number of successes, follows a Poisson process, then the number ofsuccesses in any interval is independent of the number of successes in any other interval provided the intervals

A manufacturer receives a shipment of 170 laptop computers of which 9 are defective. To test the shipment, thequality control engineer randomly selects 10 computers from the shipment and tests them. The randomvariable X represents the number of defective computers in the sample. What are the mean and standarddeviation of the random variable X?

The sum of the probabilities of a discrete probability distribution must be

Classify the following random variable according to whether it is discrete or continuous. -the cost of a road atlas

The number of goals scored at State College hockey games follows a Poisson distribution with a mean of 4goals per game. Find the probability that each of three randomly selected State College hockey games resultedin seven goals being scored.

Provide an appropriate response. -Calculate the mean for the discrete probability distribution shown here. x 2 6 8 9 P(x) 0.2 0.3 0.3 0.2

The probability that a football game will go into overtime is 15%. What is the probability that two of threefootball games will go to into overtime?

Draw the probability histogram and label the mean for n = 9 and p = 0.76.3 The Poisson Probability Distribution1 Determine if a probability experiment follows a Poisson process.

Draw the probability histogram and label the mean for n = 7 and p = 0.5

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poissondistribution with a mean of 7.5. Find the probability of observing exactly five accidents on this stretch of roadnext month.

Sixty-five percent of men consider themselves knowledgeable soccer fans. If 10 men are randomly selected,find the probability that exactly three of them will consider themselves knowledgeable fans.

A quiz consists of 780 true or false questions. If the student guesses on each question, what is the standarddeviation of the number of correct answers?

An automobile insurance company estimates the following loss probabilities for the next year on a $25,000sports car: Total loss: 0.001 50\% loss: 0.01 25\% loss: 0.05 10\% loss: 0.10 Assuming the company will sell only a $500 deductible policy for this model (i.e., the owner covers the first$500 damage), how much annual premium should the company charge in order to average $325 profit perpolicy sold?

A jury is to be selected from a pool of 40 potential jurors. The defendant faces the death penalty if convicted. Ofthe potential jurors, 5 are opposed to the death penalty and would not convict regardless of the evidence. Theprosecutor knows that if even one juror opposes the death penalty, they will have no chance of getting aconviction. If none of the jurors opposes the death penalty they will have a chance of getting a conviction. Whatis the probability that none of the jurors opposes the death penalty, if the jury consists of 12 randomly selectedjurors?