4. 1/3(3y - 6) = 8 i need the answer to this please

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

Airida [17]

Answer:

a) 24.27% probability that in a random sample of 10 people exactly 6 plan to get health insurance through a government health insurance exchange

b) 0.1% probability that in a random sample of 1000 people exactly 600 plan to get health insurance through a government health insurance exchange

c) Expected value is 560, variance is 246.4

d) 99.34% probability that less than 600 people plan to get health insurance through a government health insurance exchange

Step-by-step explanation:

To solve this question, we need to understand the binomial probability distribution and the binomial approximation to the normal.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The variance of the binomial distribution is:

$V(X) = np(1-p)$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

56% of uninsured Americans who plan to get health insurance say they will do so through a government health insurance exchange.

This means that $p = 0.56$

a. 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?

This is P(X = 6) when n = 10. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 6) = C_{10,6}.(0.56)^{6}.(0.44)^{4} = 0.2427$

24.27% probability that in a random sample of 10 people exactly 6 plan to get health insurance through a government 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?

This is P(X = 600) when n = 1000. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 600) = C_{1000,600}.(0.56)^{600}.(0.44)^{400} = 0.001$

0.1% 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?

$E(X) = np = 1000*0.56 = 560$

$V(X) = np(1-p) = 1000*0.56*0.44 = 246.4$

d. What is the probability that less than 600 people plan to get health insurance through a government health insurance exchange?

Using the approximation to the normal

$\mu = 560, \sigma = \sqrt{246.4} = 15.70$

This is the pvalue of Z when X = 600-1 = 599. Subtract by 1 because it is less, and not less or equal.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{599 - 560}{15.70}$

$Z = 2.48$

$Z = 2.48$ has a pvalue of 0.9934

99.34% probability that less than 600 people plan to get health insurance through a government health insurance exchange

4 0

2 years ago

Which value from the set (54,45,27,6) makes 54/x = 9 true?

OLga [1]

Answer:

x = 6

Step-by-step explanation:

54/6 is 9. This is the only correct one.

Hope it helps!

3 0

3 years ago

Help pls...and thank you..

Allisa [31]

Answer:

0 chance because there is no black ones but you would probably pick a yellow one bigger chance for yellow jelly bean.

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains

fenix001 [56]

So 5 liters of natural for every 7 synthetic, so 5 / 12 liters are natural oil.

so; 684 × (5/12) = 285 liters of natural oil

Hope this helps!

7 0

2 years ago

A factory producing cell phones has the following cost and revenue functions: ()=2+75+2,688 C ( x ) = x 2 + 75 x + 2 , 688 and (

prisoha [69]

Answer:

You recently joined a nature club, and last week you went on a trip with the club into the countryside. Write an email to a friend about this. In your email, you should: . describe the place in the countryside you went to with the nature club explain what you learned during the trip to the countryside . invite your friend to join you on the next nature club trip. The pictures above may give you some ideas, and you can also use some ideas of your own. Your email should be between 150 and 200 words long. You will receive up to 8 marks for the content of your email, and up to 8 marks for the language used.

Step-by-step explanation:

You recently joined a nature club, and last week you went on a trip with the club into the countryside. Write an email to a friend about this. In your email, you should: . describe the place in the countryside you went to with the nature club explain what you learned during the trip to the countryside . invite your friend to join you on the next nature club trip. The pictures above may give you some ideas, and you can also use some ideas of your own. Your email should be between 150 and 200 words long. You will receive up to 8 marks for the content of your email, and up to 8 marks for the language used.

6 0

2 years ago

4. 1/3(3y - 6) = 8 i need the answer to this please​

4. 1/3(3y - 6) = 8 i need the answer to this please