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Chapter 3: 129SE (page 209)

Scrap rate of machine parts. A press produces parts used in the manufacture of large-screen plasma televisions. If the press is correctly adjusted, it produces parts with a scrap rate of 5%. If it is not adjusted correctly, it produces scrap at a 50% rate. From past company records, the machine is known to be correctly adjusted 90% of the time. A quality-control inspector randomly selects one part from those recently produced by the press and discovers it is defective. What is the probability that the machine is incorrectly adjusted?

Short Answer

Expert verified

The probability that the machine is incorrectly adjusted is 0.53.

Step by step solution

01

Important formula

The formula for probability isP=favourableoutcomestotaloutcomes

02

The probability that the machine is incorrectly adjusted.

Here only components with a scrap rate of 5% orP(C|M)=0.05 are produced on the specified data, when the press is suitably calibrated. It produces scrap at a rate of 50% or P(C|MC)=0.5. If not calibrated correctly. The machine is known to be corrected 90% orPM=0.9 of the time from historical business registrations.

Now,

P(MC)=1-P(M)=1-0.9=0.1

And

P ( MC|C )=P ( MC) P ( C|MC )P ( MC )P ( C|MC )+P ( M )P ( C|M )=0.1+0.5(0.1)(0.5)+(0.9)(0.05)=0.53

Therefore, the probability that the machine is incorrectly adjusted is 0.53.

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Most popular questions from this chapter

Firefighter glove sizing. Human Factors (December 2015) published a study on how well firefighter gloves fit. In a group of 586 firefighters who reported their glove size, the researchers determined whether the gloves fit well or poorly by gender. The data are summarized in the accompanying table. Consider the gender and glove fit status of a randomly selected firefighter.

a. List the sample points for this experiment.

b. Assign reasonable probabilities to these sample points.

c. Find the probability the firefighter is a female.

d. Find the probability the glove fits well.

e. Find the probability the firefighter is a female and has a well-fitting glove.

f. Find the probability the firefighter is a female or has a well-fitting glove.

Glove Fits Well

Glove Fits Poorly

Totals

Males

415

132

547

Females

19

50

39

Totals

434

152

586

Source: H. Hsiao, et al., “Firefighter Hand Anthropometry and Structural Glove Sizing: A New Perspective,” Human Factors, Vol. 57, No. 8, December 2015 (Table 6).

Jamming attacks on wireless networks. Refer to the International Journal of Production Economics (Vol. 172, 2016) study of U.S. military jamming attacks on wireless networks used by terrorists, Exercise 2.8 (p. 73). Recall that 80 recent jamming attacks were classified according to network type (WLAN, WSN, or AHN) attacked and the network's number of channels (single- or multi-channel). The results are reproduced in the accompanying table.

a. Find the probability that a recent jamming attack involved a single-channel network.

b. Find the probability that a recent jamming attack involved a WLAN network.


Network Type/Number of Channels

Number of Jamming Attacks

WLAN / Single

31

WSN / Single

13

AHN / Single

8

WLAN / Multi

14

WSN / Multi

9

AHN / Multi

5

TOTAL

80

Source: S. Vadlamani et al., "Jamming Attacks on Wireless Networks: A Taxonomic Survey, "International Journal of Production Economics, Vol. 172, 2016 (Figure 6)

Investing in stocks. From a list of 15 preferred stocks recommended by your broker, you will select three to invest in. How many different ways can you select the three stocks from the 15 recommended stocks?

A sample space contains six sample points and events A, B, and C as shown in the Venn diagram. The probabilities of the sample points are

P (1) = .20, P (2) = .05, P (3) = .30, P (4) = .10,P (5) = .10, P (6) = .25.

a. Which pairs of events, if any, are mutually exclusive? Why?

b. Which pairs of events, if any, are independent? Why?

c. FindP (A∪B) by adding the probability of the sample points and then using the additive rule. Verify that the answers agree. Repeat forP (A∪C)

On-the-job arrogance and task performance. Human Performance (Vol. 23, 2010) published the results of a study that found that arrogant workers are more likely to have poor performance ratings. Suppose that 15% of all full-time workers exhibit arrogant behaviors on the job and that 10% of all full-time workers will receive a poor performance rating. Also, assume that 5% of all full-time workers exhibit arrogant behaviors and receive a poor performance rating. Let A be the event that a full-time worker exhibits arrogant behavior. Let B be the event that a full-time worker will receive a poor performance rating.

a. Are the events A and B mutually exclusive? Explain.

b. Find P(B/A).

c. Are the events A and B independent? Explain.
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