pp. 115-117—Questions 2.138, 2.143, and 2.161

2.138 BP oil leak. In the summer of 2010, an explosion on the Deepwater Horizon oil drilling rig caused a leak in one of British Petroleum (BP) Oil Company’s wells in the Gulf of Mexico. Crude oil rushed unabated for 3 straight months into the Gulf until BP could fix the leak. During the disaster, BP used suction tubes to capture some of the gushing oil. In May of 2011, in an effort to demonstrate the daily improvement in the process, a BP representative presented a graphic on the daily number of 42-gallon barrels (bbl) of oil collected by the suctioning process.

(cannot provide chart)

2.143 For each of the following data sets, compute x, s2, and s:

a. 13, 1, 10, 3, 3

b. 13, 6, 6, 0

c. 1, 0, 1, 10, 11, 11, 15

d. 3, 3, 3, 3

2.161 Velocity of Winchester bullets. The American Rifleman (June 1993) reported on the velocity of ammunition fired from the FEG P9R pistol, a 9 mm gun manufactured in Hungary. Field tests revealed that Winchester bullets fired from the pistol had a mean velocity (at 15 feet) of 936 feet per second and a standard deviation of 10 feet per sec-ond. Tests were also conducted with Uzi and Black Hills ammunition.

a. Describe the velocity distribution of Winchester bullets fired from the FEG P9R pistol.

b. A bullet, brand unknown, is fired from the FEG P9R pistol. Suppose the velocity (at 15 feet) of the bullet is 1,000 feet per second. Is the bullet likely to be manufactured by Winchester? Explain.

Nondestructive evaluation. Nondestructive evaluation

(NDE) describes methods that quantitatively characterize materials, tissues, and structures by noninvasive means, such as X-ray computed tomography, ultrasonics, and acoustic emission. Recently, NDE was used to detect defects in steel castings (JOM, May 2005). Assume that the probability that NDE detects a “hit” (i.e., predicts a defect in a steel casting) when, in fact, a defect exists is .97. (This is often called the probability of detection.) Also assume that the probability that NDE detects a hit when, in fact, no defect exists is .005. (This is called the probability of a false call.) Past experi-ence has shown a defect occurs once in every 100 steel cast-ings. If NDE detects a hit for a particular steel casting, what is the probability that an actual defect exists?

3.116 Ranking razor blades. The corporations in the highly competitive razor blade industry do a tremendous amount of advertising each year. Corporation G gave a supply of three top-name brands, G, S, and W, to a consumer and asked her to use them and rank them in order of prefer-ence. The corporation was, of course, hoping the consumer would prefer its brand and rank it first, thereby giving them some material for a consumer interview advertising campaign. If the consumer did not prefer one blade over any other but was still required to rank the blades, what is the probability that

a. The consumer ranked brand G first?

b. The consumer ranked brand G last?

c. The consumer ranked brand G last and brand W second?

3.126 Consumer recycling behavior. Refer to the Journal of Consumer Research (December 2013) study of consumer recycling behavior, Exercise 1.25 (p. 28). Recall that 78 college students were asked to dispose of cut paper they used during an exercise. Half the students were randomly assigned to list five uses for the cut paper (usefulness is salient condition), while the other half were asked to list their five favorite TV shows (control condition). The researchers kept track of which students recycled and which students disposed of their paper in the garbage. Assume that of the 39 students in the usefulness is salient condition, 26 recycled; of the 39 students in the control condition, 14 recycled. The researchers wanted to test the theory that students in the usefulness is salient condition will recycle at a higher rate than students in the control condition. Use probabilities to either support or refute the theory.

4.1 Types of random variables. Which of the following de-scribe continuous random variables? Which describe dis-crete random variables?

a. The number of newspapers sold by the New York Times each month

b. The amount of ink used in printing a Sunday edition of the New York Times

c. The actual number of ounces in a 1-gallon bottle of laundry detergent

d. The number of defective parts in a shipment of nuts and bolts

e. The number of people collecting unemployment insur-ance each month

4.2 Types of finance random variables. Security analysts are professionals who devote full-time efforts to evaluating the investment worth of a narrow list of stocks. The following variables are of interest to security analysts. Which are dis-crete and which are continuous random variables?

a. The closing price of a particular stock on the New York Stock Exchange

b. The number of shares of a particular stock that are traded each business day

c. The quarterly earnings of a particular firm d. The percentage change in earnings between last year and this year for a particular firm

e. The number of new products introduced per year by a firm