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):
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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
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