Find the indicated probabilities using the geometric distribution, the Poisson d

Question

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. A glass manufacturer finds that 1 in every 1000 glass items produced is warped. Find the probability that (a) the first warped glass item is 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 produced are defective. (a) P(the first warped glass item is the 10th item produced) = (b) P(the first warp item is the first second, or third item produced = (c) P(none of the first 10 glass items produced are defective = Which of the events are unusual? Select all that apply The event in part (a) is unusual. The event in part (b) is unusual. The event in part (c) is unusual. None of the events are unusual.

Explanation / Answer

the glass manufacturer finds that 1 in every 1000 glass produced is warped, so it is a uniform distribution from 1 to 1000 with each glass having 1/1000 probability to be warped.

(a) P( the first warped glass item is the 10th item produced) = P( early 9 is not warped0 * P( 10th item warped) = (0.999)9 * (0.001) = 0.00099

(B) first warped item is the first, second or the third item = P(1) + P(2) + P(3) = 0.001 + 0.999 * 0.001 + (0.999)2 * 0.001 = 0.00299

(c) None of the first 10 glass items are defective = 10C 0 * ( 0.999)10 = 0.99044

(d) The events A and B are unusual because of probability of that event happening is quite low, so the are unusual.

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