Question

The National Health Interview Survey reports that 44% of telephone users no longeruse landlines, and have switched completely to cell phone use. Suppose we take arandom sample of 12 telephone users. Find the probability that the sample containsexactly 5 users who have abandoned their landlines. Use the binomial probabilityformula. Write your answer with three decimal places.

Answer 1

To answer this question we will use the following formula for binomial probability:

`P(x)=\binom{n}{x}p^x(1-p)^(n-x),`

where x is the number of times for a specific outcome within n trials, and p is the probability of success on a single trial.

Substituting x=5, n=12, and p=0.44 in the above formula we get:

`P(5)=\binom{12}{5}(0.44)^5(1-0.44)^(12-5).`

Simplifying the above result we get:

`\begin{gathered} P(5)=(12!)/(5!(12-5)!)(0.44)^5(0.56)^7=792*0.44^5*0.56^7 \\ \approx0.226. \end{gathered}`

Answer: 0.226.