(a) Explanation Given: The life expectancy is 17 years. The survival of American males assuming that from age 65 follows an exponential distribution. Definition used: 1. Exponential Distribution : If X is a random variable with probability density function f ( x ) = a e − a x for x in [ 0 , ∞ ) . Then, μ = 1 a . 2. Probability density function on ( − ∞ , ∞ ) : If f is a probability density function for a random variable X in the interval ( − ∞ , ∞ ) , then 1. P ( X ≤ b ) = P ( X < b ) = ∫ − ∞ b f ( x ) d x 2. P ( X ≥ a ) = P ( X > a ) = ∫ a ∞ f ( x ) d x 3. P ( − ∞ < X < ∞ ) = ∫ − ∞ ∞ f ( x ) d x = 1 . Calculation: Given that, the probability density function is f ( x ) = a e − a x for x in [ 0 , ∞ ) . The mean of the distribution is 17 years. E ( X ) = 17 1 a = 17 a = 1 17 Substitute a = 1 17 in f ( x ) = a e − a x , f ( x ) = a e − a x </ (b) To determine To find: The probability that a randomly selected 65 years old American male will live less than 10 more years.

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Chapter 11, Problem 58RE

(a)

To determine

To find: The probability that a randomly selected 65 years old American male will live beyond 80 years of age.

(b)

To determine

To find: The probability that a randomly selected 65 years old American male will live less than 10 more years.

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Chapter 11, Problem 57RE

Chapter 11, Problem 59RE

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CALCULUS WITH APPLICATIONS

Ch. 11.1 - YOUR TURN 1 Repeat Example 1(a) for the function...Ch. 11.1 - Prob. 2YT Ch. 11.1 - Prob. 3YT Ch. 11.1 - Prob. 4YT Ch. 11.1 - Prob. 1WE Ch. 11.1 - Prob. 2WE Ch. 11.1 - Prob. 3WE Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...

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