Question

Assume that when adults with smartphones are randomly​ selected, 37​% use them in meetings or classes. If 9 adult smartphone users are randomly​ selected, find the probability that exactly 2 of them use their smartphones in meetings or classes.

A. Assume that when adults with smartphones are randomly​ selected, 41​% use them in meetings or classes. If 20 adult smartphone users are randomly​ selected, find the probability that exactly 12 of them use their smartphones in meetings or classes.

B. Assume that when adults with smartphones are randomly​ selected, 45​% use them in meetings or classes. If 6 adult smartphone users are randomly​ selected, find the probability that at least 3 of them use their smartphones in meetings or classes

Answer 1

#1.
Here, n = 9, p = 0.37, (1 - p) = 0.63 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 2)
P(X = 2) = 9C2 * 0.37^2 * 0.63^7
P(X = 2) = 0.1941

#A.
Here, n = 20, p = 0.41, (1 - p) = 0.59 and x = 12
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 12)
P(X = 12) = 20C12 * 0.41^12 * 0.59^8
P(X = 12) = 0.0417

#B.
Here, n = 6, p = 0.45, (1 - p) = 0.55 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 3).
P(X >= 3) = (6C3 * 0.45^3 * 0.55^3) + (6C4 * 0.45^4 * 0.55^2) + (6C5 * 0.45^5 * 0.55^1) + (6C6 * 0.45^6 * 0.55^0)
P(X >= 3) = 0.3032 + 0.1861 + 0.0609 + 0.0083
P(X >= 3) = 0.5585