Question

Assume that when adults with smartphones are randomly selected, 46% use them in meetings or classes. If 11 adult smartphone users are randomly selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes.

The probability 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 = 11 * 0.46
= 5.06
II.
variance = npq
where
n = total number of repetitions experiment is executed
p = success probability
q = failure probability
variance = 11 * 0.46 * 0.54
= 2.7324
III.
standard deviation = sqrt( variance ) = sqrt(2.7324)
=1.653
a.
probability that fewer than 3 of them use their smartphone in meeting or classes.
P( X < 3) = P(X=2) + P(X=1) + P(X=0)   
= ( 11 2 ) * 0.46^2 * ( 1- 0.46 ) ^9 + ( 11 1 ) * 0.46^1 * ( 1- 0.46 ) ^10 + ( 11 0 ) * 0.46^0 * ( 1- 0.46 ) ^11   
= 0.0572