(A) Explanation Given: The probability density function of the shelf life (in days) of a perishable drug which is a continuous random variable is, f ( x ) = { 800 x ( 400 + x 2 ) 2 if x ≥ 0 0 otherwise . Result used: If [ c , d ] is a subinterval of ( − ∞ , ∞ ) , then P ( c ≤ X ≤ d ) = ∫ c d f ( x ) d x , where f ( x ) is the probability density function of the continuous random variable X . Calculation: Find the probability that the drug has a shelf life of at most 20 days with lower limit − ∞ and upper limit 20. P ( − ∞ < X ≤ 20 ) = ∫ − ∞ 20 f ( x ) d x = ∫ 0 20 800 x ( 400 + x 2 ) 2 d x = 800 ∫ 0 20 x ( 400 + x 2 ) 2 d x Compute the integral by using the method of substitution as follows. Let, u = 400 + x 2 . Differentiate with respect to x on both sides of u = 400 + x 2 . d d x ( u ) = d d x ( 400 + x 2 ) d u d x = 2 x d u = 2 x d x x d x = d u 2 Obtain the limits in terms of new variable (B) To determine To find: The probability that the shelf life of a drug exceeds 15 days. (C) To determine To find: The time when the probability of the drug is still good to be 0.8.

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ISBN: 9780137400126

Author: Raymond Barnett, Michael Ziegler

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Chapter 11.2, Problem 63E

(A)

To determine

To find: The probability that the shelf life of a drug is at most 20 days.

(B)

To determine

To find: The probability that the shelf life of a drug exceeds 15 days.

(C)

To determine

To find: The time when the probability of the drug is still good to be 0.8.

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Chapter 11.2, Problem 62E

Chapter 11.2, Problem 64E

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Chapter 11 Solutions

Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)

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 that the shelf life of a drug is at most 20 days.

Solution Summary: The author calculates the probability that the shelf life of a drug is at most 20 days with lower limit -infty and upper limit 20.

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To find: The probability that the shelf life of a drug is at most 20 days.

To find: The probability that the shelf life of a drug exceeds 15 days.

To find: The time when the probability of the drug is still good to be 0.8.

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Chapter 11 Solutions