Quiz 7. March 23, 2011 Seat # _________ Name: ___ < KEY > ___ Closed book and notes. No calculator. From Problem 4--88, Montgomery and Runger, fourth edition. Assume that the distance between major cracks in a highway follows an exponential distribution with a mean of five miles. Assume that these distances are independent of each other. That is, the cracks occur according to a Poisson process. 1. (3 points) Determine the probability that there is no major crack in a randomly selected 10-mile stretch of highway. ____________________________________________________________ Let X denote the distance to the next major crack. Then X has an exponential distribution with mean 1 / λ = 5 cracks per mile. Therefore, P( X > 10) = 1 − P( X ≤ 10) = 1 − F X (10) = e − (10)(1 / 5) = e − 2 ← ____________________________________________________________ 2. (1 points) Determine the standard deviation of the distance between cracks. (Include the units)
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