Exam 4: Discrete Random Variables and Probability Distributions

If X and Y are two random variables with σ_x = 3.8,σ_y = 4.2,and Cov(X,Y)= -0.25,then Var(X + Y)= 31.58.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The finishing process on new furniture leaves slight blemishes.The following table displays a manager's probability assessment of the number of blemishes in the finish of new furniture.For each piece of furniture coming off the line it takes 15 minutes to pack for shipping.In addition,fixing the blemishes take another 2 minutes for each blemish. -On average,how long should it take between the time a piece of furniture comes off the line and is ready to ship?

The finishing process on new furniture leaves slight blemishes.The table below displays a manager's probability assessment of the number of blemishes in the finish of new furniture. On average,how many defects would we expect on a piece of furniture?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The manager of a movie rental store was interested in examining the relationship between the weekly take-home pay for a family and the amount that family spends weekly on recreational activities.The following output was generated using Minitab: Covariances Let X = weekly take-home pay,and Y = amount spent weekly on recreational activities. -Identify the variance of amount spent weekly on recreational activities.

The Poisson distribution can be used to approximate the binomial probabilities when the number of trials n is large and at the same time the probability P is:

The expected value of the sum of two random variables is the sum of their expected values.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The following table presents the probability distribution function for the number of claims processed per hour at an insurance agency. -There is a 50% chance that a newborn baby will be a boy.For families with four children,what is the probability that all the children are boys?

If two random variables X and Y are statistically independent,then Cov(X,Y)= 0.

There are 20 professors in the School of Business Administration.15 of them have received good evaluations from students,while 5 received poor evaluations.You will take four courses in the School of Business Administration next semester.What is the probability that the majority of your professors next semester have received good evaluations?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The number of people arriving at a bicycle repair shop follows a Poisson distribution with an average of 5 arrivals per hour.Let X represent the number of people arriving per hour. -What is the probability that at most seven people arrive at the bike repair shop in a one hour period of time?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: It has been reported that 1.7% of the work force will retire this year.Consider a random sample of 200 workers. -What is an estimate of the standard deviation of the number of people who will retire this year? Use the Poisson approximation to the binomial.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: It is known that 70% of the customers in a sporting goods store purchase a pair of running shoes.A random sample of 25 customers is selected.Assume that customers' purchases are made independently,and let X represent the number of customers who purchase running shoes.(Hint: Solve using Excel. ) -What is the probability that between 17 and 21 customers,inclusively,purchase running shoes?

What is the probability that no more than two customers are waiting in both lines combined?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A recent survey found that 40% of all air traffic controllers found their job extremely stressful.Suppose 12 air traffic controllers are selected at random. -What is the probability that two or more of them consider their job extremely stressful?

An auditor reviewing the invoices of a small company finds that there are errors in 1.5% of them.If the auditor looks at 500 invoices,what is the probability that he finds more than 3 invoices with errors? Use the Poisson approximation to the binomial distribution.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The number of people arriving at a bicycle repair shop follows a Poisson distribution with an average of 5 arrivals per hour.Let X represent the number of people arriving per hour. -What is the probability that between 4 and 9 people,inclusively,arrive at the bike repair shop in a one hour period of time?

The number of accidents on a US -131 highway average 4.4 per year.Assuming that the number of accidents follows a Poisson distribution,what is the probability that there are more than three accidents next year on US - 131?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The number of accidents on a particular highway averages 4.4 per year.Assume that the number of accidents follows a Poisson distribution. -What is the probability that there are exactly four accidents next year?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A company hires management trainees for entry level sales positions.Past experience indicates that only 10% will still be employed at the end of nine months.Assume the company recently hired six trainees. -What is the standard deviation of the number of trainees that will still be employed at the end of nine months?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A company hires management trainees for entry level sales positions.Past experience indicates that only 10% will still be employed at the end of nine months.Assume the company recently hired six trainees. -What is the probability that between one and three (inclusive)of the trainees will still be employed at the end of nine months?