document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=835719>Question 835719</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The life of an alkaline battery in constant use is a normally distributed random variable with mean 18 hours and standard deviation 2 hours.<BR>\n" );
document.write( "i) What is the probability that a battery tested at random lasts longer than 15 hours? <BR>\n" );
document.write( "ii) Estimate how many batteries should be purchased to have 1000 those last at least 16 hours.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #503771 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=503771\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%28x-m%29%2Fsigma=%2815-18%29%2F2=-3%2F2 ALIGN=MIDDLE  ALT=\"z=%28x-m%29%2Fsigma=%2815-18%29%2F2=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28-3%2F2%29=0.0668 ALIGN=MIDDLE  ALT=\"P%28-3%2F2%29=0.0668\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the probability it lasts longer than 15 hours is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=1-0.0668=0.9332 ALIGN=MIDDLE  ALT=\"P=1-0.0668=0.9332\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%28x-m%29%2Fsigma=%2816-18%29%2F2=-2%2F2=1 ALIGN=MIDDLE  ALT=\"z=%28x-m%29%2Fsigma=%2816-18%29%2F2=-2%2F2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28-1%29=0.158655 ALIGN=MIDDLE  ALT=\"P%28-1%29=0.158655\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "15.8655% would fail by 16 hours so 84.135% would survive.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2FX=.84135 ALIGN=MIDDLE  ALT=\"1000%2FX=.84135\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=1188.573 ALIGN=MIDDLE  ALT=\"X=1188.573\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You should buy 1189 batteries.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );