document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137717>Question 1137717</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal​ distribution, with a mean of 17 minutes and a standard deviation of 3 minutes.<BR>\n" );
document.write( "​(a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take​ longer, the customer will receive the service for​ half-price. What percent of customers receive the service for​ half-price?<BR>\n" );
document.write( "​(b) If the automotive center does not want to give the discount to more than 7​% of its​ customers, how long should it make the guaranteed time​ limit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755604 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=755604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the mean is 17 minutes and the standard deviation is 3 minutes.\r<BR>\n" );
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document.write( "the probability that it will take longer than 20 minutes is .1587.\r<BR>\n" );
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document.write( "that means that almost 16% of the customers would receive half price.\r<BR>\n" );
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document.write( "if the automotive service does not want to give the discount to more than 7% of its customers, then the guarenteed time limits has to be greater than 21.428 minutes.\r<BR>\n" );
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document.write( "these figures were derived using the following normal distribution calculator.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "here's a display of the results.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/033011.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/033012.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the first display calculates area from a value.\r<BR>\n" );
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document.write( "the second display calculates value from an area.\r<BR>\n" );
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document.write( "if you use the calculator with x-scores, the mean is 0 and the standard deviation is 1.\r<BR>\n" );
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document.write( "if you use the calculator with raw scores, as i did above, the mean is the mean of your distribution and the standard deviation is the standard deviation of your distribution.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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