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Exam 4: Discrete Random Variables and Probability Distributions

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Question 91

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The quality of computer disks is measured by sending the disks through a certifier which counts the number of missing pulses.A certain brand of computer disks averages 0.1 missing pulse per disk.Let the random variable X denote the number of missing pulses. -Find the probability the next inspected disk will have no missing pulse.

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Question 92

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Let the random variable X denote the number of children who do not recognize their mother's voice.Find the variance of X.

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Question 93

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Consider the following probability distribution.Which of the following is true?

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. -What is the variance of the time it takes between the time a piece of furniture comes off the line and is ready to ship?

Let the random variable Y = a + bX.Then,μ_Y = bμ_X.

The standard deviation of a discrete random variable σ is the positive square root of its:

Are X and Y statistically independent? Explain.

What is the probability that no one is waiting or being served in the regular checkout line?

Continue to assume that the returns of the four stocks are no longer independent of one another,and the correlations between all pairs of stock returns are as given in the second question.Now,suppose that this investor decides to place $20,000 each in stocks B and D,and $10,000 each in stocks A and C.Find the mean and standard deviation of the total amount that this investor earns in one year from these four investments.

What is the standard deviation for the number of people catching a cold?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Consider the following probability distribution function. -What is P(2 < X < 5)?

The covariance of two variables X and Y:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: In a shipment of 18 trucks to a local truck dealer,there are four trucks that don't have air conditioning.Assume that you select four trucks at random. -In Detroit metropolitan area,past records revealed that only 20 percent of all the high school graduates go to college.From 20 graduates selected at random,what is the probability that exactly 5 will go to college?

When sampling without replacement from a finite population such that the probability of a success is no longer constant from trial to trial,the data must follow a:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Suppose you know that the number of complaints coming into a phone center averages 4.2 every ten minutes.Assume that the number of calls follows the Poisson distribution. -What is the probability that there are three or fewer calls during the next ten minutes?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: On average,an RV sales lot sells six RVs per month.Assume the number of sales of RVs per month follows the Poisson distribution. -What is the probability that exactly six RVs are sold next month?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: As a purchasing agent,you are responsible for selecting sources of supply for manufactured components to use in your firm's production process.The salesman for a certain supplier has indicated that they can supply an electronic sub-assembly that has a defect rate of 1.1%-well below your current supplier's defect rate.You accept 100 sub-assemblies for evaluation,and find that there were four defects. -Using the Poisson approximation to the binomial,how likely is it to get four or less defects out of 100?

The number of phone calls arriving at a phone center each day is an example of a continuous random variable.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: On average,you receive 2.6 pieces of junk mail a day.Assume that the number of pieces of junk mail you receive each day follows the Poisson distribution. -What is the probability of receiving more than three pieces of junk mail today?

A strong linear relationship is defined as a condition where the individual observation points are close to a straight line.