Question

assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey). If 8 adult smartphone users are randomly selected, find the probability that exactly 6 of them use their smartphones in meetings or classes.

Answer 1

Explanation:

Given:

p=54 %=0.54

n=8

DEFINITIONS

Definition binomial probability:

`P(X=x)=(n !)/(x !(n-x) !) \cdot p^(x) \cdot(1-p)^(n-x)`

Complement rule:

P( not A) = 1- P(A)

`Addition rule for disjoint or mutually exclusive events`

`P(A \text { or } B)=P(A)+P(B)`

Evaluate the definition of binomial probability at x=6

`P(X=6)=(8 !)/(6 !(8-6) !) \cdot 0.54^(6) \cdot(1-0.54)^(8-6)=28 \cdot 0.54^(6) \cdot 0.46^(2) \approx 0.1469`