document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=569959>Question 569959</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the Internal Revenue Service is studying the category of charitable contributions. A sample of 32 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 32 returns 7 had charitable contributions of more than $1,000. Suppose 6 of these returns are selected for a comprehensive audit.\r<BR>\n" );
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document.write( "(a)What is the probability exactly one of the six audited had a charitable deduction of more than $1,000?\r<BR>\n" );
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document.write( "(b)What is the probability at least one of the audited returns had a charitable contribution of more than $1,000?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #367481 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=367481\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A sample of 32 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 32 returns 7 had charitable contributions of more than $1,000. <BR>\n" );
document.write( "p-hat = 7/32<BR>\n" );
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document.write( "Suppose 6 of these returns are selected for a comprehensive audit. <BR>\n" );
document.write( "(a)What is the probability exactly one of the six audited had a charitable deduction of more than $1,000? <BR>\n" );
document.write( "Binomial with n = 6 and p(had) = 7/32 ; p(not had) = 25/32<BR>\n" );
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document.write( "P(x = 1) = 6C1(7/32)(25/32)^5 = binompdf(6,7/32,1) = 0.3820<BR>\n" );
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document.write( "(b)What is the probability at least one of the audited returns had a charitable contribution of more than $1,000?<BR>\n" );
document.write( "P(at least one) = 1 - P(none)<BR>\n" );
document.write( "= 1 - (5/32)^6<BR>\n" );
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document.write( "= 1 - 0.0000146<BR>\n" );
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document.write( "= 0.9999<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( " </SPAN>\n" );
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