a. Explanation Calculation: It is given that for a laser in cytometry machine, the time to failure follows an exponential distribution with λ = 0.00004 . The random variable X follows the exponential distribution with parameter λ . Then the probability density function is, f ( x ) = λ e − λ x for x > 0 Let, the random variable X denotes the time to failure for a laser in cytometry machine. The probability density function is, f ( x ) = 0.00004 e − 0.00004 x for x > 0 The probability that the time until failure is at least 20,000 hours: P ( X > 20 , 000 ) = ∫ 20 , 000 ∞ ( 0 b. To determine Find the probability that the time until failure is at most 30,000 hours. c. To determine Find the probability that the time until failure is between 20,000 and 30,000 hours.

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

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Question

Chapter 4, Problem 198SE

To determine

Find the probability that the time until failure is at least 20,000 hours.

To determine

Find the probability that the time until failure is at most 30,000 hours.

To determine

Find the probability that the time until failure is between 20,000 and 30,000 hours.

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Chapter 4, Problem 197SE

Chapter 4, Problem 199SE

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Chapter 4 Solutions

Applied Statistics and Probability for Engineers

Ch. 4.2 - 4-1. Suppose that f(x) = e−x for 0 < x. Determine...Ch. 4.2 - 4-2. Suppose that f (x) = 3(8x – x2)/256 for 0< x...Ch. 4.2 - 4-3. Suppose that f (x) = 0.5 cos x for −π/2 < x <...Ch. 4.2 - Prob. 4E Ch. 4.2 - 4-5. Go Tutorial Suppose that for 3 < x < 5....Ch. 4.2 - Prob. 6E Ch. 4.2 - 4-7. Suppose that f(x) = 1 .5x2 for −1 < x < 1....Ch. 4.2 - 4-8. The probability density function of the time...Ch. 4.2 - 4-9. The probability density function of the net...Ch. 4.2 - Prob. 10E

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