Question

Consider a binomial probability distribution with p = 0.2. Complete parts a through c below. a. Determine the probability of

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Answer:

Given that:

Consider a binomial probability distribution with p=0.2

p = 0.2

1 - p = 1 - 0.2 = 0.8

(a)  Determine the probability of exactly three successes when n=4.

n = 4

Using binomial probability formula ,

P(X = 1) =(n C x) p (1-pn-1

P(X = 3) =(4 C 3) (0.2) (0.8)

P(X = 3) = 4 * 0.008 * 0.8

P(X = 3) = 0.0256

probability = 0.0256

(b)  Determine the probability of exactly three successes when n=6

n = 6

Using binomial probability formula ,

P(X = 1) = (n C x) p (1-pn-1

P(X = 3) =(6 C 3) (0.2)-(0.8)

P(X =3) = 20 * 0.008* 0.512

P(X = 3) = 0.0819

probability = 0.0819

(c) Determine the probability of exactly three successes when n= 7

n = 7

Using binomial probability formula ,

P(X = 1) =(n C x) p (1-pn-1

P(X = 3) =(7 C 3) (0.2) (0.8)

P(X =3) = 35 * 0.008 * 0.4096

P(X = 3) = 0.1146

probability = 0.1146

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