Explanation Given: The time taken by the rat for finding the path through the maze is distributed exponentially. The average time taken by the rat to find the path is 30 seconds. Formula used: Improper integrals: “If f is continuous over the indicated interval and the limit exist, then ∫ a ∞ f ( x ) = lim b → ∞ ∫ a b f ( x ) d x ”. Exponential probability density function: “For a continuous random variable X , f ( x ) = { ( 1 λ ) e − x λ if x ≥ 0 0 otherwise and F ( x ) = { 1 − e − x λ if x ≥ 0 0 otherwise , where f ( x ) is the probability density function and F ( x ) is the cumulative distribution function and λ is mean”. Calculation: Let X be the random variable which represents the time taken by the rat for finding the path through the maze. The average time taken by the rat is 30 seconds, that is, λ = 30 seconds. Therefore, the exponential probability density function X is given by f ( x ) = { ( 1 30 ) e − x 30 if x ≥ 0 0 otherwise } . The rat finds the way through the maze in 1 minute, that is, 1 ( 60 ) = 60 seconds. Therefore, the value of x is equal to x = 60

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Chapter 11.4, Problem 84E

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To find: The probability for a rat to find the path through the maze in more than 1 minute.

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Chapter 11.4, Problem 83E

Chapter 11.4, Problem 85E

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Chapter 11 Solutions

EBK CALCULUS FOR BUSINESS, ECONOMICS, L

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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The probability for a rat to find the path through the maze in more than 1 minute.

Solution Summary: The author explains that the probability for a rat to find the path through the maze in more than 1 minute is approximately 0.135

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