Question

1a). Assume that when adults with smartphones are randomly selected,61 % use them in meetings or classes. If 15 adult smartphone users are randomly selected, find the probability that exactly 11 of them use their smartphones in meetings or classes. I need help getting the probability of this.

b). Assume that when adults with smartphones are randomly selected, 47 % use them in meetings or classes. If 14 adult smartphone users are randomly selected, find the probability that fewer than 33 of them use their smartphones in meetings or classes. I need help getting the probability of this. Thanks again for the help!

Answer 1

1.
a.
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 = 15 * 0.61
= 9.15
II.
variance = npq
where
n = total number of repetitions experiment is executed
p = success probability
q = failure probability
variance = 15 * 0.61 * 0.39
= 3.5685
III.
standard deviation = sqrt( variance ) = sqrt(3.5685)
=1.889

the probability that exactly 11 of them use their smartphones in meetings or classes
P( X = 11 ) = ( 15 11 ) * ( 0.61^11) * ( 1 - 0.61 )^4
= 0.1374

b.
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 = 14 * 0.47
= 6.58
II.
variance = npq
where
n = total number of repetitions experiment is executed
p = success probability
q = failure probability
variance = 14 * 0.47 * 0.53
= 3.4874
III.
standard deviation = sqrt( variance ) = sqrt(3.4874)
=1.8675

the probability that fewer than 3 of them use their smartphones in meetings or classes
P( X < 3) = P(X=2) + P(X=1) + P(X=0)   
= ( 14 2 ) * 0.47^2 * ( 1- 0.47 ) ^12 + ( 14 1 ) * 0.47^1 * ( 1- 0.47 ) ^13 + ( 14 0 ) * 0.47^0 * ( 1- 0.47 ) ^14   
= 0.0117