depakote is a medication whose sole purpose is to reduce pain associated with mi

Question

depakote is a medication whose sole purpose is to reduce pain associated with migrain headaches. In clinical trials of Depakote, 5% of the patients in the study experience weight as a side effect. A random sample of 10 depakote users is obtained, and the number of patients who experience weight gain is recorded. a) Find the probability that exactly 3 experience weight gain as a side effect. b)Find the probability that 3 or fewer experience weight gain as a side effect c)find the probability that 4 or more experience weight gain as a side effect. Find the probability that between 1 and 4 patients, inclusive experience weight gain as a side effect.

Explanation / Answer

Given,

5% of the patients in the study experience that weight is a side effect.

p = 0.05

sample has 10 observations

n = 10

a) p(x=3)

we use binomial distribution

nCr p^r q^(n-r)

10C3 * 0.05^3 * 0.95*(10-3)

= 0.0104

b) p(x<=3)

= p(x=0)+p(x=1)+p(x=2)+p(x=3)

= 10C0 * 0.05^0 * 0.95*(10-0) + 10C1 * 0.05^1 * 0.95*(10-1) + 10C2 * 0.05^2 * 0.95*(10-2) + 10C3 * 0.05^3 * 0.95*(10-3)

= 0.9989

c) p(X>=4)

p(x=4)+P(x=5)+...P(x=10)

= 0.000102

D) P(X>=1 & X<=4)

P(X=1) + P(X=2) +P(X=3)+P(X=4)

P(X<=4) - P(X=0)

= 0.9999363 - 0.598736

= 0.4012

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