Question

1. Assume that when adults with smartphones are randomly​ selected, 56​% use them in meetings or classes. If 5 adult smartphone users are randomly​ selected, find the probability that at least 2 of them use their smartphones in meetings or classes.

2. Assume that when adults with smartphones are randomly​ selected, 56​% use them in meetings or classes. If 12 adult smartphone users are randomly​ selected, find the probability that fewer than 4 of them use their smartphones in meetings or classes.

Answer 1

Solution:

( 1 )

n = 5

p = 0.56

binomial probability distribution

Formula:

P_{(k out of n )}= n!*p^k * q^n-k / k! *(n - k)!

P( x 2 ) =  5!*0.56² * 0.44^5-2 / 2! *(5 - 2)!+ 5!*0.56³ * 0.44^5-3 / 3! *(5 - 3)!

+ 5!*0.56⁴ * 0.44^5-4 / 4! *(5 - 4)!+ 5!*0.56⁵ * 0.44^5-5 / 5! *(5 - 5)!

= 0.2671+0.3400+0.2164+0.0551

= 0.8786

( 2 )

n = 12

p = 0.56

binomial probability distribution

Formula:

P_{(k out of n )}= n!*p^k * q^n-k / k! *(n - k)!

P( x < 4 ) = 12!*0.56³ * 0.44^12-3 / 3! *(12 - 3)!+ 12!*0.56² * 0.44^12-2 / 2! *(12 - 2)!

+ 12!*0.56¹ * 0.44^12-1 / 1! *(12 - 1)!+ 12!*0.56⁰ * 0.44^12-0 / 0! *(12 - 0)!

= 0.0239+0.0056+0.0008+0.0001

= 0.0304