Question

The lifetime of a machine that is used in the production process is exponentially distributed with a mean of 4,000 hours. a. What is the probability the machine will last more than 4,250 hours? b. What is the probability the machine will fail within the first 3,250 hours? a. P(useful life more than 4,250 hours) = (Round to four decimal places as needed.) b. P(useful life less than or equal to 3,250 hours) = (Round to four decimal places as needed.) 

          The lifetime of a machine that is used in the production process is exponentially distributed with a mean of 4,000 hours.
a. What is the probability the machine will last more than 4,250 hours?
b. What is the probability the machine will fail within the first 3,250 hours?

a. P(useful life more than 4,250 hours) =
(Round to four decimal places as needed.)

b. P(useful life less than or equal to 3,250 hours) =
(Round to four decimal places as needed.)
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The lifetime of a machine that is used in the production process is exponentially distributed with a mean of 4,000 hours. a. What is the probability the machine will last more than 4,250 hours? b. What is the probability the machine will fail within the first 3,250 hours? a. P(useful life more than 4,250 hours) = (Round to four decimal places as needed.) b. P(useful life less than or equal to 3,250 hours) = (Round to four decimal places as needed.)

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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The lifetime of a machine that is used in the production process is exponentially distributed with a mean of 4,000 hours. a. What is the probability the machine will last more than 4,250 hours? b. What is the probability the machine will fail within the first 3,250 hours? a. P(useful life more than 4,250 hours) = (Round to four decimal places as needed.) b. P(useful life less than or equal to 3,250 hours) = (Round to four decimal places as needed.)
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The lifetime of a machine that is used in the production process is exponentially distributed with a mean of 4,000 hours. a. What is the probability the machine will last more than 4,250 hours? b. What is the probability the machine will fail within the first 3,250 hours? a. P(useful life more than 4,250 hours) = (Round to four decimal places as needed.) b. P(useful life less than or equal to 3,250 hours) = (Round to four decimal places as needed.)

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Transcript

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00:02 Let x be the lifetime of a machine, comma, x e to the power of x be 4000.
00:26 For exponential with mean theta, f x is equal to 1 by theta, e to the power minus x by theta, comma, x is less than theta.
00:55 P bracket, x is less than theta, is equal to e to the power minus t by theta, and p x is greater than t is equal to one minus e to the power minus t by theta...
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