Explanation Given information: Pr ( X ≤ 4 ) = 0.75 , f ( x ) = k e − k x . Explanation: A random variable X is the relief times (in minutes) of arthritic patients who have taken an analgesic for their pain. It follows an exponential distribution with the density function f ( x ) = k e − k x A certain analgesic provides relief within 4 minutes for 75% of a large group of patients, that is Pr ( X ≤ 4 ) = 0.75 . Pr ( X ≤ 4 ) = 0.75 ⇒ ∫ 0 4 f ( x ) d x = 0.75 ⇒ ∫ 0 4 k e − k x d x = 0.75 ⇒ k ∫ 0 4 e − k x d x = 0.75 ⇒ k ( e − k x − k ) | 0 4 = 0

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Chapter 12, Problem 19RE

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The value for k in the exponential density function, when Pr(X≤4)=0.75

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The value for k in the exponential density function, when Pr ( X ≤ 4 ) = 0.75

Solution Summary: The author explains that the value of constant k in the exponential density function is 0.35.

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