This Quiz: 9 pts A machine breaks down at random times at an average rate of 0.2

Question

This Quiz: 9 pts A machine breaks down at random times at an average rate of 0.2 times per day a. What is the probability that the next break down will be more than 8 days from now? (Round your answer to four decimal places) b. Wha: 's the probability that the next break down will be less than 10 days from now? (Round your answer to four decimal places) D c. What is the probability that in a 13 day period there will be exactly 7 breakdowns? (Round your answer to four decimal places) [ d. What is the average number of days until the next break down? Round your answer to one decimal place.) e. What is the variance of the number of days until the next break down? Round your answer to one decimal place f, what is the average number of break downs in a given 13-day period? (Round your answer to one decimal place ) g. What is the variance of the number of break downs in a given 13-day period? Round your answer to one decimal place ,) 9

Explanation / Answer

Exponential Distribution

a) P(X > 8) = 1 - P(X <= 8) = 1 - (1 - e-*x) = 1 - (1 - e-0.2*8) = 0.2019

b) P(X <= 10) = 1 - e-0.2*10 = 0.8647

c) Poisson distribution, = 0.2*13 = 2.6 times per 13 days

P(X = 7) = ke-/k! = 2.67*e-2.6/7! = 0.01184

d) Mean exponential distribution, E[X] = 1/ = 1/0.2 = 5 days per breakdown

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