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 #593969 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=593969\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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.\r<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" );
document.write( "z(16) = (16-13.8)/4.3 = 2.2/4.3 = 0.5116<BR>\n" );
document.write( "P(x < 16) = P(z<0.5116) = normalcdf(-100,0.5116) = 0.6955<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 accounts are paid off in less than that time.<BR>\n" );
document.write( "Find the z-value with a right-tail of 0.95<BR>\n" );
document.write( "invnorm(0.95) = 1.645<BR>\n" );
document.write( "Find the corresponding time value::<BR>\n" );
document.write( "x = 1.645*4.3+13.8 = 20.87<BR>\n" );
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document.write( "(c) The company has just received 29 invoices. Find the probability that the mean payoff time for these invoices is more than 16 days.<BR>\n" );
document.write( "t(16) = (16-13.8)/[4.3/sqrt(29)] = 2.7552<BR>\n" );
document.write( "P(x > 16) = P(t> 2.7552 when df = 28) = tcdf(2.7552,100,28) = 0.005<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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