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Chapter 4: Q163S (page 281)

Which of the following describe discrete random variables, and which describe continuous random variables?

a. The number of damaged inventory items

b. The average monthly sales revenue generated by a salesperson over the past year

c. Square feet of warehouse space a company rents

d. The length of time a firm must wait before its copying machine is fixed

Short Answer

Expert verified

a. This is a discrete random variable.

b. This is a discrete random variable.

c. This is a continuous random variable.

d. This is a continuous random variable.

Step by step solution

01

Given information

The variables are random variables.

02

Identifying the random variable in case the number of damaged inventory items

a.

.Since the number of damaged inventory items can be counted, these are discrete random variables.

03

Identifying the random variable in case the average monthly sales revenue generated by a salesperson over the past year

b.

Average monthly sales can be counted. So, the average monthly sales revenue generated by a salesperson over the past year is a discrete random variable.

04

Identifying the random variable in case the square feet of warehouse space a company rents

c.

The square feet of warehouse are measurable but within an interval. So, the square feet of warehouse space a company rents is a continuous random variable.

05

Identifying the random variable in case the length of time a firm must wait before its copying machine is fixed

d.

The length of time can be measurable but within an interval. Hence, the length of time a firm must wait before its copying machine is fixed is a continuous random variable.

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Most popular questions from this chapter

Checkout lanes at a supermarket. A team of consultants working for a large national supermarket chain based in the New York metropolitan area developed a statistical model for predicting the annual sales of potential new store locations. Part of their analysis involved identifying variables that influence store sales, such as the size of the store (in square feet), the size of the surrounding population, and the number of checkout lanes. They surveyed 52 supermarkets in a particular region of the country and constructed the relative frequency distribution shown below to describe the number of checkout lanes per store, x.

a. Why do the relative frequencies in the table represent the approximate probabilities of a randomly selected supermarket having x number of checkout lanes?

b. FindE(x) and interpret its value in the context of the problem.

c. Find the standard deviation of x.

d. According to Chebyshev’s Rule (Chapter 2, p. 106), what percentage of supermarkets would be expected to fall withinμ±σ? withinμ±2σ?

e. What is the actual number of supermarkets that fall within? ? Compare your answers with those of part d. Are the answers consistent?

Executive networking and firm performance. Refer to the Journal of Accounting Public Policy (Vol. 34, 2015) study of the impact of executive networking on firm performance, Exercise 2.101 (p. 117). Recall that firm performance was measured as annual return on equity (ROE), recorded as a percentage. The mean ROE for the firms studied was 13.93%, and the standard deviation was 21.65%. Assume that these values represent m and s for the population ROE distribution and that this distribution is normal. What value of ROE will be exceeded by 80% of the firms?

Consider the discrete probability distribution shown here:

  1. Find μ=E(x).
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  3. Find the probability that the value of x falls within one standard deviation of the mean. Compare this result to the Empirical Rule.

Hospital patient interarrival times. The length of time between arrivals at a hospital clinic has an approximately exponential probability distribution. Suppose the mean time between arrivals for patients at a clinic is 4 minutes.

a. What is the probability that a particular interarrival time (the time between the arrival of two patients) is less than 1 minute?

b. What is the probability that the next four interarrival times are all less than 1 minute?

c. What is the probability that an interarrival time will exceed 10 minutes?

Preventative maintenance tests. The optimal schedulingofpreventative maintenance tests of some (but not all) ofnindependently operating components was developed in Reliability Engineering and System Safety(January2006).The time (in hours) between failures of a component wasapproximated by an exponential distribution with meanθ.

a. Supposeθ=1000 hours. Find the probability that the time between component failures ranges between 1200and1500hours.

b. Again, assumeθ=1000hours. Find the probability that the time between component failures is at least1200hours.

c. Given that the time between failures is at leastrole="math" localid="1658214710824" 1200 hours, what is the probability that the time between failures is less than1500hours?
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