document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971479>Question 971479</A>: <I><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "8.  An accountant is studying the time it takes a company to make payments on accounts payable.  The mean time it takes to pay off an invoice is 13.8 days with a standard deviation of 4.3 days, and the times are normally distributed.<BR>\n" );
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document.write( "(a)  What is the probability that an account is paid off in less than 16 days?<BR>\n" );
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document.write( "(b)  Find the 95th percentile for the payoff time- that is, a time for which 95% of the<BR>\n" );
document.write( "accounts are paid off in less than that time.<BR>\n" );
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document.write( "(c)  The company has just received 29 invoices.  Find the probability that the mean payoff<BR>\n" );
document.write( "time for these invoices is more than 16 days. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593967 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=593967\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean=13.8 d   SD=4.3 d\r<BR>\n" );
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document.write( "z< (16-13.8)/4.3 =(2.2/4.3)\r<BR>\n" );
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document.write( "z<0.51<BR>\n" );
document.write( "p=0.695\r<BR>\n" );
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document.write( "95% from the left is z=1.645<BR>\n" );
document.write( "z* sd= 1.645 *4.3=7.07 days\r<BR>\n" );
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document.write( "13.8+7.07=20.9 days\r<BR>\n" );
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document.write( "z>(16-13.8)/(4.3/sqrt(29))<BR>\n" );
document.write( "z>2.2/.798  =2.755\r<BR>\n" );
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document.write( "p=0.003\r<BR>\n" );
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document.write( "One invoice can certainly be more than 16 days but the MEAN of 16 of them is far less likely.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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