A certain drug causes liver damage in 0.5% of patients. Suppose the drug is to b

Question

A certain drug causes liver damage in 0.5% of patients. Suppose the drug is to be tested on 100 patients. Answer the following questions. a. Find an approximate probability that none of these patients will experience liver damage. b. Find an approximate probability that 1 of these patients will experience liver damage. c. Find an approximate probability that 2 or more of these patients will experience liver damage. d. Find the exact probabilities of the above three questions and compare them with the approximate probabilities

Explanation / Answer

X = number of patient who will experience liver damage.

X follow binomial distribution

with n = 100, p = 0.005

but it can be approximated to poisson distribution with mean = np = 100*0.005 = 0.5

a) Find an approximate probability that none of these patients will experience liver damage.

P(X =0) =

b. Find an approximate probability that 1 of these patients will experience liver damage.

P(X =1) = 0.304407

c. Find an approximate probability that 2 or more of these patients will experience liver damage.

=1 - P(x =0) -P(X =1)

=   0.90204

d. Find the exact probabilities of the above three questions and compare them with the approximate probabilities

exact

P(X = 0) = 0.995^100

= 0.60577

P(X =1) = 0.304407

P(X >=2) = 0.089822

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