Question

Given that there is a probability of 0.85 that a randomly selected adult knows what Twitter is, find an estimate of the probability of getting exactly two adults who know what Twitter is when 10 adults are randomly selected. Find the mean and variance of the number of adults who know what Twitter is.

Answer 1

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
I.
mean = np
where
n = total number of repetitions experiment is executed
p = success probability
mean = 10 * 0.85
= 8.5
II.
variance = npq
where
n = total number of repetitions experiment is executed
p = success probability
q = failure probability
variance = 10 * 0.85 * 0.15
= 1.275
III.
standard deviation = sqrt( variance ) = sqrt(1.275)
=1.12916

estimate of the probability of getting exactly two adults who know what Twitter is
P( X = 2 ) = ( 10 2 ) * ( 0.85^2) * ( 1 - 0.85 )^8
= 0.00001

Mean = 8.5
standard deviation = 1.12916
variance =1.275