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. (Select the correct graph.)

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

d-Find σ (in terms of the number of syringes). (Enter a number. Round your answer to three decimal places.)

Please show work and correct answer

Answer 1

Ans:

a)

Use binomial distribution with n=12 and p=0.01

P(x=r)=¹²C_r*0.01^r*(1-0.01)^12-r

r	P(r)
0	0.8864
1	0.1074
2	0.0060
3	0.0002
4	0.0000
5	0.0000
6	0.0000
7	0.0000
8	0.0000
9	0.0000
10	0.0000
11	0.0000
12	0.0000

c)

P(accepted)=P(x<=1)=(1-0.01)^12+¹²C₁*0.01*(1-0.01)^11=0.994

d)standard deviation,sigma=sqrt(12*0.01*(1-0.01))=0.345