SOLUTION: According to a report from the Center for Studying Health System Change, 20% of Americans delay or go without medical care because of concerns about cost (The Wall Street Journal,

Question 1085716: According to a report from the Center for Studying Health System Change, 20% of Americans delay or go without medical care because of concerns about cost (The Wall Street Journal, June 26, 2008). Suppose eight individuals are randomly selected.

Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
Question:
According to a report from the Center for Studying Health System Change, 20% of Americans delay or go without medical care because of concerns about cost (The Wall Street Journal, June 26, 2008). Suppose eight individuals are randomly selected.
[NOTE: Question incomplete. Will calculate probability of all possible outcomes, i.e. 0-8 respondents have financial concerns]

Solution:
Looks like a binomial distribution, let's check:
1. Bernoulli trials, i.e. exactly two possible outcomes. (yes, have concerns, or not)
2. Number of trials is known before experiment, i.e. independent of outcomes. (yes, 8)
3. All trials are independent of each other. (yes, randomly selected)
4. Probability of success is known, and remain constant throughout trials. (yes, large population, small sample)
Conclusion: binomial distribution applies.

Let
N=sample size = 8
x=number of successes (have financial concern)
p=probability of success, 0.2
q=probability of failure, 1-0.2=0.8 (Bernoulli trials, either success or not)
C(N,x)=number of combinations of x objects selected from N = N!/(x!(N-x)!)
then
P(x)=C(N,x)(p^x)(q^(N-x))
for each of x=0 to 8.
For example, N=8, x=2,
P(2)=C(8,2)(0.2^2)(0.8^6)=0.29360

The complete set of probabilities is as follows:
P(0)=0.16777
P(1)=0.33554
P(2)=0.29360
P(3)=0.14680
P(4)=0.04585
P(5)=0.00916
P(6)=0.00115
P(7)=8.19200*10^-5
P(8)=2.56000*10^-6
sum=1.0
RELATED QUESTIONS
According to a report from the Center for Studying Health System Change, 20% of Americans (answered by stanbon)

The National Health Center of health Statistics reported that for every 800 deaths in... (answered by ewatrrr)

the national health center of health statistics reported that for every 800 students in... (answered by ikleyn)

According to a local survey 80% of Americans own a car. If you randomly select 3... (answered by FrankM)

To win at LOTTO in a certain state, one must correctly select 6 numbers from a... (answered by ikleyn)

According to a recent study, the proportion of Americans who can order a meal in a... (answered by ewatrrr)

In problems on the model of one already solved -- Car rental agency A will rent a compact (answered by ankor@dixie-net.com)

In 2006 the number of Americans who were members of a health club was 42.7 million. This (answered by drj)

Bayside insurance offers two health plans. Under plan A, Giselle would have to pay the... (answered by mananth)