Submit QU his Question: 1 pt 16 of 20 (14 complete) This Quiz: 20 pts possi Find

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Submit QU his Question: 1 pt 16 of 20 (14 complete) This Quiz: 20 pts possi Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities produced, (b) the first warped item is the first, second, or third item produced, and (c) none of the first 10 glass items produced are defective. (a) P(the first warped glass item is the 12th item produced)- A glass manufacturer finds that 1 in every 200 glass items produced is warped. Find the probability that (a) the first warped glass item is the 12th item (Round to three decimal places as needed.) (b) P(the first warped item is the first, second, or third item produced)- Round to three decimal places as needed.) (c) P(none of the first 10 glass items produced are defective) Round to three decimal places as needed.) Which of the events are unusual? Select all that apply A. The event in part (a) is unusual k to select your answer(s)

Explanation / Answer

Ans:

We will use geometric distribution(as number of trials till first success)

p=1/200=0.005

a)P(x=12)=(1-0.005)^11*0.005=0.005

b)P(x=1,2,3)=0.005+0.995*0.005+0.995^2*0.005=0.015

For part c use binomial distribution with n=10,p=0.005

c)P(x=0)=0.995^10=0.951

As,in part a and b,probabilities are less than 0.05,so part a) and b) are unusual events

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