Exam P Practice Problem 27 – Exponential Distributions

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Problem 27A

For a certain brand of light bulbs, the time (in thousands of hours) until the instant a light bulb burns out follows an exponential distribution. From past experience, we know that \displaystyle \frac{1}{4} of the light bulbs will go out within 500 hours of use. What proportion of the light bulbs can be expected to go out within 1000 hours of use?

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Problem 27B

In the emergency room of a large hospital in a metropolitan area, the wait time (in hours) to see a doctor follows an exponential distribution. From past experience, 40% of the wait times are 3 hours or less. What proportion of the patients in the emergency room can be expected to wait more than 15 hours to see a doctor?

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Answers

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