An experiment is designed to test the potency of a drug on 20 rats. Previous ani

Question

An experiment is designed to test the potency of a drug on 20 rats. Previous animal studies have shown that a 10-mg drug is lethal 5% the time within the first 4 hours; of the animals alive at 4 hours, 10% will die in the next 4 hours. (a) What is the probability that 3 or more rats will die in the first 4 hours? (b) Suppose 2rats die in the first 4 hours. What is the probability 2 or fewer rats will die in the next 4 hours? (c) What is the probability that 0 rats will die in the 8-hour period? (d) What is the probability that 1 rat will die in the 8-hour period? (e)Can you write a general formula for the probability that x rats will die in the 8-hour period?

Explanation / Answer

here we use binomial distribution and for binomial distribution with parameter n and p

P(X=x)=nCxpx(1-p)n-x

(a) here p=0.05 and n=20

P(X>=3)=1-P(X<=2)=1-0.9245=0.0755

P(X<=2)=0.9245 ( using ms-excel command =BINOMDIST(2,20,0.05,1))

(b) both events are independents so here we use n=20 and p=0.1

P(x<=2)=0.6769 ( using ms-excel command =BINOMDIST(2,20,0.1,1))

(c) here we use n=20 and p=0.1

P(X=0)=0.1216 ( using ms-excel command =BINOMDIST(2,20,0.1,0))

(d)

here we use n=20 and p=0.1

P(X=0)=0.2701 ( using ms-excel command =BINOMDIST(2,20,0.1,1))

(e) n=20 and p=0.1

P(X=x)=20Cx(0.1)x(1-0.1)n-x

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