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Firdavs [7]
3 years ago
11

According to a 2014 Gallup poll, 56% of uninsured Americans who plan to get health insurance say they will do so through a gover

nment 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?
Mathematics
1 answer:
alexgriva [62]3 years ago
7 0

Answer:

0.2427 is the required probability.        

Step-by-step 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

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