1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ad-work [718]
2 years ago
7

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.
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?
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?
Mathematics
1 answer:
Airida [17]2 years ago
4 0

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

You might be interested in
a taxi driver charges $2.25 per mile. the driver also charges a one time $12 fee. write and solve an equation to determine how m
Andrew [12]

Answer:

if x is the number of miles driven, the equation is 2.25x + 12=30. solved: x = 8 miles

Step-by-step explanation:

First, you make the equation. If x is the number of miles, the price per mile would be 2.25 times x or 2.25x. You also have to add the one time fee of $12, so you have 2.25x + 12. Next, you're trying to find x if it costs $30 total so you would have 2.25x + 12 = 30.

Solving,

2.25x + 12 = 30

subtract 12 from both sides

2.25x = 18

divide both sides by 2.25

x = 8 miles

8 0
3 years ago
Please help me please please please
AURORKA [14]

Answer:

y= -9

try desmos for questions like these it saved my life.

Step-by-step explanation:

6 0
3 years ago
Mr. Hudkins wants his 6th grade math class to memorize their multiplication facts. He decides to increase the number of facts th
Maksim231197 [3]

Answer: m = 15w

Step-by-step explanation: The reason why the answer is m = 15w is because since he said "He decides to increase the number of facts they are expected to memorize each week." Which makes it so that only the  multiplication fact increased to 15 since they wouldn't put it lower then that. And there is a 2nd reason why the multiplication fact is 15. the reason why is because theres only one answer with 30 and its completely wrong. So therefore,, The answer is Multiplication Fact = 15weeks.

8 0
3 years ago
Read 2 more answers
Koleman just received a 6% raise in salary. Before the raise he was making $52,000 per year. How much more will Koleman earn nex
pogonyaev

$52,000 + 6% = $55,120

If this helped you, would you mind answering one of my recent questions? Thanks!

7 0
3 years ago
Read 2 more answers
What is 8.239 rounded to the tenths place.
andriy [413]
8.239 rounded to the nearest tenths = 8.2
8 0
3 years ago
Other questions:
  • Credit cards place a three digit security code on the back of cards. What is the probability that a code starts with the number
    10·1 answer
  • Give 3 solutions on 14x+7y=28 that will satisfy the consistent systems
    7·2 answers
  • Olive walks at a rate of 4 miles per hour she lives 2 miles from the mews station how long wil it talk her to walk home from the
    6·1 answer
  • What is the value of n=9x12+3x25-8
    9·2 answers
  • The order of these two reflections (select matter. The resulting image (select) the same for a
    5·1 answer
  • I need help solving this :/
    14·1 answer
  • Help!!!!!! Find the center and radius of the circle.
    9·1 answer
  • A rectangle has a length of 12 meters and a width of 400 centimeters. What is the perimeter,
    8·2 answers
  • There are 16 pool balls on the table. If you shoot all of the solid balls in on the first turn how many different ways can they
    14·1 answer
  • PLEASE HELP QUICK MY CLASS IS ALMOST OVER!!!!!!!1<br> The value of -4 2 is _____.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!