document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166765>Question 1166765</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Shorty’s Muffler advertises it can install a new muffler in 30 minutes or less.  However, the work standards department at corporate headquarters recently conducted a study and found that 20% of the mufflers were not installed in 30 minutes or less.  The Maumee branch installed 50 mufflers last month.  If the corporate report is correct:<BR>\n" );
document.write( "a.	How many of the installations at the Maumee branch would you expect to take more than 30 minutes?<BR>\n" );
document.write( "b.	What is the likelihood that fewer than 8 installations took more than 30 minutes?<BR>\n" );
document.write( "c.	What is the likelihood that 8 or fewer installations too more than 30 minutes?<BR>\n" );
document.write( "d.	What is the likelihood that exactly 8 of the 50 installations took more than 30 minutes?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791604 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=791604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is a binomial with n=50 and p=0.20 (failure)<BR>\n" );
document.write( "would expect 10 (50*).20 to have taken more than 30 minutes.<BR>\n" );
document.write( "exactly 8 taking more is 50C8*0.20^8*0.80^42 or probability 0.1169<BR>\n" );
document.write( "fewer than 8 would be <= 7 and that probability would be 0.1904\r<BR>\n" );
document.write( "\n" );
document.write( "calc binompdf(50,0.2.8) for the first<BR>\n" );
document.write( "binomcdf (50,0.2,7) for the second.\r<BR>\n" );
document.write( "\n" );
document.write( "normal approximation mean is 10<BR>\n" );
document.write( "variance is 10*0.8 or 8<BR>\n" );
document.write( "sd is sqrt(8) or 2.828<BR>\n" );
document.write( "less than 8 would be z<(7.5-10)/2.828  or -0.88 and that probability is 0.1894, a decent estimate. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );