document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=974111>Question 974111</A>: <I><SPAN STYLE=\"word-break: break-all;\"> USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counsel people on parole. Let us say success means a person does not become a repeat offender. Alice has been given a group of four parolees.<BR>\n" );
document.write( "(a) Find the probability P(r) of r successes ranging from 0 to 4. (Round your answers to three decimal places.)<BR>\n" );
document.write( "P(0) =  <BR>\n" );
document.write( "P(1) =  <BR>\n" );
document.write( "P(2) =  <BR>\n" );
document.write( "P(3) =   <BR>\n" );
document.write( "P(4) =  \r<BR>\n" );
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document.write( "(c) What is the expected number of parolees in Alice's group who will not be repeat offenders? (Round your answer to two decimal places.)<BR>\n" );
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document.write( "What is the standard deviation? (Round your answer to two decimal places.)\r<BR>\n" );
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document.write( "(d) How large a group should Alice counsel to be about 98% sure that three or more parolees will not become repeat offenders?<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 #596128 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=596128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counsel people on parole. Let us say success means a person does not become a repeat offender. Alice has been given a group of four parolees.<BR>\n" );
document.write( "(a) Find the probability P(r) of r successes ranging from 0 to 4. (Round your answers to three decimal places.)<BR>\n" );
document.write( "P(0) = 4C0*(0.75)^0*0.25^4<BR>\n" );
document.write( "P(1) = 4C1*(0.75)*0.25^3<BR>\n" );
document.write( "P(2) = 4C2*(0.75)^2 * 0.25^2<BR>\n" );
document.write( "P(3) = etc.<BR>\n" );
document.write( "P(4) = etc.\r<BR>\n" );
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document.write( "(c) What is the expected number of parolees in Alice's group who will not be repeat offenders? (Round your answer to two decimal places.)<BR>\n" );
document.write( "Ans: mean = np = 4*0.75 = 3<BR>\n" );
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document.write( "What is the standard deviation? (Round your answer to two decimal places.)<BR>\n" );
document.write( "Ans: std = sqrt[npq] = sqrt[3*0.25] = (1/2)sqrt(3)<BR>\n" );
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document.write( "(d) How large a group should Alice counsel to be about 98% sure that three or more parolees will not become repeat offenders?<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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