Question

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. The ABC Electronics Company has just manufactured 2100 write-rewrite CDs, and 50 are defective. If 6 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?

Answer 1

Answer: The probability that the entire batch will be accepted is 0.832.

Step-by-step explanation:

Since we have given that

Number of CDs = 2100

Number of defective CDs = 50

he entire batch is accepted if every item in the sample is okay.

So, we will use "Binomial theorem":

p be the probability of success i.e. no defect.

So, $p=\dfrac{2100-50}{2100}=\dfrac{2050}{2100}=0.97$

q be the probability of failure i.e. defect.

So, $q=\dfrac{50}{2100}=0.02$

so, Number of CDs selected = 6

so, it becomes,

$P(X=6)=^6C_6p^6q^0=(0.97)^6=0.832$

Hence, the probability that the entire batch will be accepted is 0.832.