Question

8.With one method of a procedure called acceptance​ sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. A company has just manufactured 1591 ​CDs, and 196 are defective. If 3 of these CDs are randomly selected for​testing, what is the probability that the entire batch will be​ accepted? Does this outcome suggest that the entire batch consists of good​ CDs? Why or why​ not?

If 3 of these CDs are randomly selected for​ testing, what is the probability that the entire batch will be​accepted? The probability that the whole batch is accepted is____

​(Round to three decimal places as​ needed.)

9. The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a​ student's alarm clock has a 10.1​% daily failure rate. Complete parts​ (a) through​ (d) below.

a. What is the probability that the​ student's alarm clock will not work on the morning of an important final​ exam?

​(Round to three decimal places as​ needed.)

b. If you have two such alarm clocks, what is the probability that they both will fail on some morning?

Answer 1

8.

Probability that a random CD is defective = 196/1591

$\therefore$  Probability that the entire batch is accepted = Probability that three randomly selected CDs are not defective

= [1-(196/1591)]³ = 0.674

This does not suggest that the entire batch consists of good CDs. This is because that it is evident the entire batch is accepted in spite of having 196 defective CDs. All the units may well be selected from non-defective part of the batch, and the entire batch is the considered to be non-defective, in spite of actually having a pretty 12.3% defective units.

.

9.

Daily failure rate = 10.1% = 0.101

a.

Probability that the​ student's alarm clock will not work on the morning of an important final​ exam = 0.101

b.

Probability that they both alarm clocks will fail on some morning = 0.101$\times$0.101 = 0.010201