document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=773759>Question 773759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with explanation:\r<BR>\n" );
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document.write( "The time spent on customer service calls in normally distributed with a mean of 4.5 minutes.\r<BR>\n" );
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document.write( "1)  You are given that the probability that a call will take less that 5 minutes is equal to 60%.  What is the probability that a call will take between 4.5 and 5 minutes.\r<BR>\n" );
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document.write( "2)  You are given that the a call will take more than 3 minutes is equal to 80%.  What is the probability what a call will take more than 6 minutes.\r<BR>\n" );
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document.write( "Struggling with this.\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #471847 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=471847\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) the probability that a call will take less that 5 minutes is equal to 60%. What is the probability that a call will take between 4.5 and 5 minutes\r<BR>\n" );
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document.write( "Pr(4.5<X<5) = Pr(X<5) - Pr(X>4.5)<BR>\n" );
document.write( "by definition of the mean Pr(X>4.5) is 50%<BR>\n" );
document.write( "Pr(4.5<X<5) = 60% - 50% = 10% <BR>\n" );
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document.write( "2) You are given that the a call will take more than 3 minutes is equal to 80%. What is the probability what a call will take more than 6 minutes. <BR>\n" );
document.write( "Pr(X>3) = 1 - Pr(X<3) = 80%  and Pr(X<3) = 20%<BR>\n" );
document.write( "need to calculate std dev<BR>\n" );
document.write( "z-value = (3 - 4.5) / std. dev<BR>\n" );
document.write( "consult Z table for 20% probability = -.84<BR>\n" );
document.write( "-.84 = -1.5 / std. dev <BR>\n" );
document.write( "std. dev = 1.5/.84 = 1.78<BR>\n" );
document.write( "now<BR>\n" );
document.write( "Pr(X>6) = 1 - Pr(X<6)<BR>\n" );
document.write( "z-value = (6 -4.5) / 1.78 = .84<BR>\n" );
document.write( "Pr(X<6) = 80%<BR>\n" );
document.write( "Pr(X>6) = 1 - Pr(X<6)= 1 -.80 = 20%\r<BR>\n" );
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