Consider a binomial probability with p=0.2. Complete parts a through c below. a.

Question

Consider a binomial probability with p=0.2. Complete parts a through c below. a. Determine the probability of exactly two successes when n=5. b. Determine the probability of exactly two successes when n=6. Consider a binomial probability with p=0.2. Complete parts a through c below. a. Determine the probability of exactly two successes when n=5. b. Determine the probability of exactly two successes when n=6. Consider a binomial probability with p=0.2. Complete parts a through c below. a. Determine the probability of exactly two successes when n=5. b. Determine the probability of exactly two successes when n=6.

Explanation / Answer

BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials   
n = is the number of independent trials   
p = probability of success on each trial
a.
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 5 * 0.2
= 1
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 5 * 0.2 * 0.8
= 0.8
III.
standard deviation = sqrt( variance ) = sqrt(0.8)
=0.8944
P( X = 2 ) = ( 5 2 ) * ( 0.2^2) * ( 1 - 0.2 )^3
= 0.2048
b.
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 6 * 0.2
= 1.2
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 6 * 0.2 * 0.8
= 0.96
III.
standard deviation = sqrt( variance ) = sqrt(0.96)
=0.9798
P( X = 2 ) = ( 6 2 ) * ( 0.2^2) * ( 1 - 0.2 )^4
= 0.2458

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