Question

The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of twelve syringes taken from the batch. Suppose the batch contains 5% defective syringes.
(b) Find ?. (Enter your answer to two decimal places.)
What is the expected number of defective syringes the inspector will find? (Enter your answer to two decimal places.)
(c) What is the probability that the batch will be accepted? (Round your answer to three decimal places.)
(d) Find ?. (Round your answer to three decimal places.)

Answer 1

Answer:

Step-by-step explanation:

p = 0.05 ( or 5%)

n = 12

Part b)

Expected value = n X p

expected value = 12 X 0.05

Expected value = 0.60

Part c)

Batch will be accepted if the number of defectives is less than 2

P(accepted) = P( x = 0) + P (x = 1)

where x = number of defectives

From binomial formula;

P(X=x) = nCx X p^x X (1-p)^(n-x)

we got n = 12, p = 0.05

P(x=0) = 12C0 X 0.05^0 X (0.95)^12

P(x=0) = 0.54036

P(x=1) = 12C1 X (0.05)61 X (0.95)^11

P(x=1) = 0.34128

P(accepted) = 0.54036 + 0.34128

P(accepted) = 0.88164

Part d)

Standard deviation = √(0.05 X 0.95/12) = 0.062915