Score: 0.5 of 1 pt 9 of 13 (13 complete) Score: 91.03%, 11.83 of 13 pts 4.3.17 F

Question

Score: 0.5 of 1 pt 9 of 13 (13 complete) Score: 91.03%, 11.83 of 13 pts 4.3.17 Find the indicated probabilitios using the geometric distribution, the Poisson distribution, or the binomial distrbution. Then defermine if the A glass manufacturer finds that 1 in every 250 glass ilems produced is warped. Find the probablity that (a) the first warped glass item is E, Question Help | * If convenient, use the appropriate probabiity table or technology to find the probabilities. events are the 10th item produced, (b) the first warped item is the first, second, or third item produced, and (c) none of the first 10 glass items (a) Pithe first warped glass itom is the 10th item produced) 0.004 Round to three decimal places as needed.) (b) Pithe first warped tem is the first, second, or third item producod)- 0.012 (Round to three decimal places as needed) (c) Ptnone of the first 10 glass items produced are detective)- Round to three decimal places as needed.) 12 part 1 Clear All

Explanation / Answer

Binomial distribution

a)

Probability that the glass item is warped, p = 1/250 = 0.004

Required probability = (1-p)^9 * p = (1-0.004)^9*0.004 = 0.004

b)
if 3 items are selected, probability that none is warped = (1-p)^3 = 0.988

Hence required probability = 1 - 0.988 = 0.012

c)
probability that none of the item is defective = (1-p) = 0.996

Required probability = 0.996^10 = 0.961

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