According to a 2014 Gallup poll. 56% of uninsured Americans who plan to get heal

Jerold

Jerold

Answered question

2021-09-28

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.
a) What is the probability that in a random sample of 10 people exactly 6 plan to get health insurance through a goverment health insurance exchange?
b) What is the probability that in a random sample of 1000 people exactly 600 plan to get health insurance through a government health insurance exchange?
c) What are the expected value and the variance of X?
d) What is the probability that less than 600 people plan to get health insurance through a government health insurance exchange?

Answer & Explanation

Jozlyn

Jozlyn

Skilled2021-09-29Added 85 answers

Step 1
As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost other parts in the next question.
Let X be the number of people who plan to get health insurance through a govt health insurance plan X follow Binomial with n=10,p=0.56
Step 2
(a) Let X be the number of people who plan to get health insurance through a govt health insurance plan X follow Binomial with n=10,p=0.56
The probability mass function of Binomial distribution is
P(X=x)=(nx)px(1p)nx
To find, P(X=6)
P(X=6)=(106)0.566(10.56)106
=0.2427
The probability that exactly 6 out of 10 plan to get health insurance through a govt health insurance plan is 0.2427
(b) Let X be the number of people who plan to get health insurance through a govt health insurance plan
X follow Binomial with n=1000,p=0.56
The probability mass function of Binomial distribution is
P(X=x)=(nx)px(1p)nx
To find, P(X=600)
P(X=600)=(1000600)0.56600(10.56)1000600
=0.0010
(Note : using excel formula for Binomial probability "=BINOM.DIST(600,1000,0.56,FALSE)"
Probability that exactly 600 out of 1000 plan to get a health insurance through a govt health insurance plan is 0.0010
c) E(X)=np=10000.56=560
V(X)=np(1p)=10000.560.44=246.4
Expected value of X=560
Variance of X=246.4
To find P(X<600)
P(X<600)=x=0599(1000x)0.56x(10.56)1000x
=0.9942
(Note : using excel formula for Binomial probability "=BINOM.DIST(599,1000,0.56,TRUE)"
The probability that less than 600 out of 1000 plan to get health insurance through a govt health insurance plan is 0.9942)

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school probability

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?