(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.

14th Edition

ISBN: 9780134856667

Author: Stocker

Publisher: VST

See similar textbooks

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could co…

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a…

Videos

Question

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.2, Problem 62E

Chapter 11.2, Problem 64E

Students have asked these similar questions

on donne f(x) da fonction derive dhe do fonction fcsos calcule f'(x) orans chacun des Cas sulants: 3 1) f(x)=5x-11, 2- f (x) = ->³ 3-1(x) = x² 12x +π; 4-f(x)=- 5-f(x) = 33-4x6-609)=-3x²+ 7= f(x) = x + 1.8-f(x) = 4 s-f(x) = x++ X+1 -x-1 2 I 3x-4 дево

13. Check to see if the following set of functions is orthogonal on the interval [-3, 3] with respect to the integral inner product. Show all work. Recall that a set of functions is orthogonal if all pairs of functions are orthogonal. Пх COS 3 {cos (), sin().1} 3

Need help solving please!

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

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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.

Concept explainers

Videos

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.

Want to see the full answer?

Chapter 11 Solutions