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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鈥�(鈥�MC|C鈥�)=P鈥�(鈥�MC)鈥�P鈥�(鈥�C|MC鈥�)P鈥�(鈥�MC鈥�)P鈥�(鈥�C|MC鈥�)+P鈥�(鈥�M鈥�)P鈥�(鈥�C|M鈥�)=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

Working on summer vacation.Refer to the Harris Interactive(July 2013) poll of whether U.S. adults workduring summer vacation, Exercise 3.13 (p. 169). Recall thatthe poll found that 61% of the respondents work duringtheir summer vacation, 22% do not work at all while onvacation, and 17% were unemployed. Also, 38% of thosewho work while on vacation do so by monitoring theirbusiness emails.

a.Given that a randomly selected poll respondent will work while on summer vacation, what is the probability that the respondent will monitor business emails?

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