document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085716>Question 1085716</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699843 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=699843\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question:<BR>\n" );
document.write( "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.<BR>\n" );
document.write( "[NOTE: Question incomplete.  Will calculate probability of all possible outcomes, i.e. 0-8 respondents have financial concerns]<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "Looks like a binomial distribution, let's check:<BR>\n" );
document.write( "1. Bernoulli trials, i.e. exactly two possible outcomes. (yes, have concerns, or not)<BR>\n" );
document.write( "2. Number of trials is known before experiment, i.e. independent of outcomes. (yes, 8)<BR>\n" );
document.write( "3. All trials are independent of each other. (yes, randomly selected)<BR>\n" );
document.write( "4. Probability of success is known, and remain constant throughout trials. (yes, large population, small sample)<BR>\n" );
document.write( "Conclusion: binomial distribution applies.<BR>\n" );
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document.write( "Let<BR>\n" );
document.write( "N=sample size = 8<BR>\n" );
document.write( "x=number of successes (have financial concern)<BR>\n" );
document.write( "p=probability of success, 0.2<BR>\n" );
document.write( "q=probability of failure, 1-0.2=0.8 (Bernoulli trials, either success or not)<BR>\n" );
document.write( "C(N,x)=number of combinations of x objects selected from N = N!/(x!(N-x)!)<BR>\n" );
document.write( "then<BR>\n" );
document.write( "P(x)=C(N,x)(p^x)(q^(N-x))<BR>\n" );
document.write( "for each of x=0 to 8.<BR>\n" );
document.write( "For example, N=8, x=2,<BR>\n" );
document.write( "P(2)=C(8,2)(0.2^2)(0.8^6)=0.29360<BR>\n" );
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document.write( "The complete set of probabilities is as follows:<BR>\n" );
document.write( "P(0)=0.16777<BR>\n" );
document.write( "P(1)=0.33554<BR>\n" );
document.write( "P(2)=0.29360<BR>\n" );
document.write( "P(3)=0.14680<BR>\n" );
document.write( "P(4)=0.04585<BR>\n" );
document.write( "P(5)=0.00916<BR>\n" );
document.write( "P(6)=0.00115<BR>\n" );
document.write( "P(7)=8.19200*10^-5<BR>\n" );
document.write( "P(8)=2.56000*10^-6<BR>\n" );
document.write( "sum=1.0 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );