(a) Explanation Given information: Probability density function is f ( t ) = { 1 15 , 676 t 2 e − 0.05 t if 0 ≤ t ≤ 150 0 otherwise . Calculation: Show the function as follows: f ( t ) = 1 15 , 676 t 2 e − 0.05 t (1) Find the probability that an infected patient will display symptoms within the first 48 hours P ( 0 ≤ X ≤ 48 ) as shown below. P ( 0 ≤ X ≤ 48 ) = ∫ 0 48 f ( t ) d t = ∫ 0 48 1 15 , 676 t 2 e − 0.05 t d t = 1 15 , 676 ∫ 0 48 t 2 e − 0.05 t d t (2) Show the method of integration by parts as shown below: ∫ u d v = u v − ∫ v d u (3) Consider u = t 2 Differentiate both sides of the Equation. d u = 2 t d t Consider d v = e − 0.05 t d t Integrate both sides of the Equation. v = − 1 0.05 e − 0.05 t Apply method of integration by parts as shown below. Substitute t 2 for u , e − 0.05 t for dv , 2t dt for du , and − 1 0.05 e − 0.05 t for v in Equation (3). ∫ t 2 e − 0.05 t d t = t 2 × ( − 1 0.05 e − 0.05 t ) − ∫ ( − 1 0.05 e − 0.05 t ) 2 t d t = − t 2 0.05 e − 0.05 t + 2 0.05 ∫ t e − 0.05 t d t = − 20 t 2 e − 0.05 t + 40 ∫ t e − 0.05 t d t (4) Consider u = t Differentiate both sides of the Equation. d u = d t Consider d v = e − 0 (b) To determine To find: The probability that an infected patient will not display symptoms until after 36 hours.

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ISBN: 9781337613927

Author: Stewart

Publisher: CENGAGE L

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Chapter 8.5, Problem 12E

(a)

To determine

To find: The probability that an infected patient will display symptoms within the first 48 hours.

(b)

To determine

To find: The probability that an infected patient will not display symptoms until after 36 hours.

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Chapter 8.5, Problem 11E

Chapter 8.5, Problem 13E

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Chapter 8 Solutions

Calculus, Early Transcendentals

Ch. 8.1 - Use the arc length formula (3) to find the length...Ch. 8.1 - Use the arc length formula to find the length of...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Find the exact length of the curve. 9....Ch. 8.1 - Find the exact length of the curve. 10....

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The probability that an infected patient will display symptoms within the first 48 hours.

Solution Summary: The author explains that the probability that an infected patient will display symptoms within the first 48 hours is 0.439.

To find: The probability that an infected patient will display symptoms within the first 48 hours.

To find: The probability that an infected patient will not display symptoms until after 36 hours.

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Chapter 8 Solutions