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 1% defective syringes.(a) Make a histogram showing the probabilities of

r = 0, 1, 2, 3,   ,

11 and 12 defective syringes in a random sample of twelve syringes.

(b) Find μ. (Enter your answer to two decimal places.)
μ =

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 σ. (Round your answer to three decimal places.)
σ = syringes

Answer 1

Solution-A:

Rcode:

library(tigerstats)
pbinomGC(c(0,12),region="between",size=12,prob=0.01,graph=TRUE)

Solution-B:

mean=np=12*0.01 =0.12

the expected number of defective syringes the inspector will find=0.12

(c) What is the probability that the batch will be accepted? (Round your answer to three decimal places.)

plant will reject a batch of syringes if two or more defective syringes are found in a batch of 12

It will be accepted when 0 or 1 defectives found

P(X=0)+P(X=1)

Rcode:

library(tigerstats)
pbinomGC(c(0,1),region="between",size=12,prob=0.01,graph=TRUE)

0.994

is the probability that the batch will be accepted=0.994

Solution-d:

standard deviation=sqrt(n*p*(1-p)

=sqrt(12*0.01*(1-0.01))

=4.32

standard deviation=4.32