Question

According to a recent poll 80% of millenials sleep with their cell phone next to their bed. (Millenials are commonly defined as people born 1980-1999.) Suppose you seleet a random sample of five millenials. a, What is the probability that exactily four millenials in your sample sleep next to their cell phone? b. What is the probability that more than three millenials in your sample sleep next to their cell phone?

Answer 1

Let $X=$ the number of millenials sleeping with their cell phone next to their bed $X\sim Bin(n,p)$

$$P(X=x)=\dbinom{n}{x}p^x(1-p)^{n-x}$$

Given $p=0.8, n=5$

a.

$$P(X=4)=\dbinom{5}{4}0.8^4(1-0.8)^{5-4}=0.4096$$

b.

$$P(X>3)=P(X=4)+P(X=5)=$$

$$=\dbinom{5}{4}0.8^4(1-0.8)^{5-4}+\dbinom{5}{5}0.8^5(1-0.8)^{5-5}=$$

$$=0.4096+0.32768=0.73728$$