document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163008>Question 163008</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately mound-shaped and symmetric, with a mean of  72 jobs and a standard deviation of  6. <BR>\n" );
document.write( "Where do we expect approximately 95% of the distribution to fall?  <BR>\n" );
document.write( "(Compute the interval that will contain 95% of the data).\r<BR>\n" );
document.write( "\n" );
document.write( "Z= (0.95-72)/6= -71.05/6= -11.86  ? (I wasn’t sure about this one or it might     be 6 because the distribution is known)\r<BR>\n" );
document.write( "\n" );
document.write( "Is this correct or how do I work it out- I would greatly appreciate the help- thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120138 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=120138\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's denote the confidence interval as (L,U) where \"L\" is the lower limit of the confidence interval and \"U\" is the upper limit of the confidence interval\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It's very helpful to remember that within 2 standard deviations of the mean lies 95% of the population. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=2 ALIGN=MIDDLE  ALT=\"z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (see below)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The simplest way to produce a confidence interval is to use the formulas <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=mu-z%2Asigma ALIGN=MIDDLE  ALT=\"L=mu-z%2Asigma\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U=mu%2Bz%2Asigma ALIGN=MIDDLE  ALT=\"U=mu%2Bz%2Asigma\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu ALIGN=MIDDLE  ALT=\"mu\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the mean and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma ALIGN=MIDDLE  ALT=\"sigma\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the standard deviation, and \"z\" is the number of standard deviations away from the mean (ie the z score).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note: there are other ways to calculate the confidence interval\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=72-2%2A6=72-12=60 ALIGN=MIDDLE  ALT=\"L=72-2%2A6=72-12=60\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U=72%2B2%2A6=72%2B12=84 ALIGN=MIDDLE  ALT=\"U=72%2B2%2A6=72%2B12=84\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that our confidence interval is (60,84)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );