A textile manufacturing process finds that on average, four flaws occur per ever

Question

A textile manufacturing process finds that on average, four flaws occur per every 80 yards of material produced.

a. What is the probability of exactly two flaws in a 80-yard piece of material? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

b. What is the probability of no more than two flaws in a 80-yard piece of material? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

c. What is the probability of no flaws in a 50-yard piece of material? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

Explanation / Answer

Ans:

Use poisson distribution with 4 flaws per every 80 yards

a)

P(x=2)=e-4*(42/2!)=0.1465

b)

P(x<=2)=P(x=0)+P(x=1)+P(x=2)

=e-4*(40/0!+41/1!+42/2!)

=e-4*(1+4+8)

=0.2381

c)on average there will be=(4/80)*50=2.5 flaws per 50 yard

P(x=0)=e-2.5*(2.50/0!)=0.0821

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