Question

According to a 2014 Gallup poll, 56% of uninsured Americans who plan to get health insurance say they will do so through a government health insurance exchange. What is the probability that in a random sample of 10 people exactly 6 plan to get health insurance through a government health insurance exchange?

Answer 1

0.2427 is the required probability.

Explanation:

We are given the following information:

We treat americans who plan to get health insurance through a government health insurance exchange as a success.

P(Americans who plan to get health insurance) = 56% = 0.56

Then the number of Americans follows a binomial distribution, where

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

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 6 and x = 10

We have to evaluate:

`P(x = 6)\\= \binom{6}{10}(0.56)^6(1-0.56)^4\\=0.2427`

Thus, 0.2427 is the probability that in a random sample of 10 people exactly 6 plan to get health insurance through a government health insurance exchange