6. 1/2.5 points | Previous Answers BBUnderStat10 5.3.010. My Notes Ask Your Teac

Question

6. 1/2.5 points | Previous Answers BBUnderStat10 5.3.010. My Notes Ask Your Teacher 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 seven syringes taken from the batch. Suppose the batch contains 5% defective syringes. (a) Make a histogram showing the probabilities of. 0, 1, 2, 3, seven syringes. , 6 and 7 defective syringes in a random sample of 0.3 03 Pir) 02 0.1 0.7 0.6 05 0.3 0.25 02 0.15 0.4 0.3 0.05 (b) Find . (Enter your answer to two decimal places.) -35 -syringes 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.)

Explanation / Answer

defective is success

problem on binomial probability with n=7 and p=0.05

Mean=0.35

Solutionb:

Expected number of defective syringes=np=7*0.35=2.45

Expected number of defective syringes=2 syringes

Solutionc:

P(X>=2)

=P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)

=0.0406+0.0036+0.0002+0.000005+0+0

=0.044

answer:0.044

Solutiond:

For BInomila distr

std dev=sqrt(npq)

=sqrt(7*0.05*0.95)

=0.577

ANSWER:0.577

x 0 1 2 3 4 5 6 7 P(x=x) 0.6983 0.2573 0.0406 0.0036 0.0002 0.000005 0 0

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