Explanation Given: The number of successive dry days that occur after a rainstorm is random variable that is randomly distributed exponentially with a mean of 8 days. Approach: If X is a random variable, then the probability density function of an exponential distribution is given as f ( x ) = a e − a x for x ∈ [ 0 , ∞ ) and P ( a ≤ X ≤ b ) = ∫ a b f ( x ) d x . Calculation: The probability density function of an exponential distribution is given as f ( x ) = a e − a x . Since, μ = 1 a and μ = 8 , the a = 1 8 . Therefore, the probability density function of an exponential distribution is given as f ( x ) = 1 8 e − 1 8 x To determine b. To find: The probability that fewer than 2 dry days occur after a rainstorm.

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ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 13.3, Problem 49E

To determine

a.

To find:

The probability that 10 or more successive dry days occur after a rainstorm.

To determine

b.

To find:

The probability that fewer than 2 dry days occur after a rainstorm.

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Chapter 13.3, Problem 48E

Chapter 13.3, Problem 50E

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Chapter 13 Solutions

Calculus For The Life Sciences

Ch. 13.1 - Repeat Example 1a for the function f(x)=2x2 on...Ch. 13.1 - Prob. 2YT Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E

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a. To find: The probability that 10 or more successive dry days occur after a rainstorm.

Solution Summary: The author explains that the probability that 10 or more successive dry days occur after a rainstorm is 0.2865.