In the field of quality control, the science of statistics is often used to dete

Question

In the field of quality control, the science of statistics is often used to determine if a process is "out of control." Suppose the process is, indeed, out of control and 19% of items produced are defective. (a) If three items arrive off the process line in succession, what is the probability that all three are defective? (b) If four items arrive in succession, what is the probability that three are defective? (a) The probability is (Round to four decimal places as needed.) (b) The probability is (Round to four decimal places as needed.)

Explanation / Answer

Solution(a)

Probability of defective item =0.19

P(x=3,3)= 3C3 *(0.19)^3 * (0.81)^0

= 1* 0.006859*1

=0.006859

So probability is 0.6859%

Solution(b)

P(X=3,4)= 4C3 *(0.19)^3 *(0.81)

=4*0.19*0.19*0.19*0.81

= 0.02222

So probability is 2.222%

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