Question

an insurance company reported that 50% of adults stated they are distracted by their smartphones while driving. 9 adult drivers selected randomly, determine the probability that exactly 4 of them are distracted.

Answer 1

Step-by-step explanation:

Adults distracted by their smartphones = 50%

To get probability of exacty 4 adults getting distracted, we would apply binomial distribution

p = 50% = 0.5

Probability of exacty 4 adults getting distarcted = P(x = 4)

`\begin{gathered} P\mleft(x=x\mright)=^nC_{x\text{ }}p^xq^(n-x) \\ x\text{ = 3} \\ n\text{ = 9} \\ q\text{ = 1- p }=\text{ 1- 50\%} \\ q\text{ = 50\% = 0.5} \end{gathered}`

Inserting the values:

`P(x^{}=4)=^9C_4\text{ }*(0.5)^4*(0.5)^(9-4)`