document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1084647>Question 1084647</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A supermarket manager wishes to make an estimate of the average time in minutes a customer spends at the checkout counter. It is known from previous studies that the variance is 10.8. How large a sample is required if she wants a 95% confidence interval for the population mean that extends no further than 0.7 minutes from the sample mean. Round up your answer to a whole number. \r<BR>\n" );
document.write( "\n" );
document.write( "I gound the answer to be 8468 but it is incorrect. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #698712 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=698712\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"4\"><BR>\n" );
document.write( "The formula to be used is<BR>\n" );
document.write( "n = ( (z*sigma)/E )^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "where,<BR>\n" );
document.write( "n = min sample size needed<BR>\n" );
document.write( "z = critical value drawn from the standard normal (Z) distribution<BR>\n" );
document.write( "sigma = population standard deviation<BR>\n" );
document.write( "E = margin of error desired\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "At 95% confidence, we can find the z critical value to be approximately z = 1.96<BR>\n" );
document.write( "Look at the <a  rel=nofollow HREF=\"http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">statistics table</a>. <BR>\n" );
document.write( "Locate \"95%\" at the bottom where the confidence levels are. The value just above \"95%\" is \"1.960\" which is the same as 1.96<BR>\n" );
document.write( "A table like the one I have linked is often found in the back of any statistics textbook. <BR>\n" );
document.write( "So this is why z = 1.96, which is approximate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The variance is given to be 10.8. Take the square root of the variance to get the standard deviation (sigma)<BR>\n" );
document.write( "sigma = sqrt(variance)<BR>\n" );
document.write( "sigma = sqrt(10.8)<BR>\n" );
document.write( "sigma = 3.286335345031<BR>\n" );
document.write( "which is approximate\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The error desired is E = 0.7 because we want the upper or lower end of the confidence interval to be at most 0.7 units away from the center xbar.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Summarizing what we have so far:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z = 1.96<BR>\n" );
document.write( "sigma = 3.286335345031<BR>\n" );
document.write( "E = 0.7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Plug those three values mentioned above into the formula below\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n = ( (z*sigma)/E )^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n = ( (1.96*3.286335345031)/0.7 )^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n = ( (6.44121727626076)/0.7 )^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n = ( 9.2017389660868 )^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n = 84.6720000000002\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n = 85 <font color=blue>Round up to the nearest whole number</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Min Sample Size: n = 85\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "On the last step, we ALWAYS round up regardless of the decimal portion. <BR>\n" );
document.write( "This rounding up is to ensure that we clear the hurdle. <BR>\n" );
document.write( "If we rounded down, then E > 0.7, which is too large. <BR>\n" );
document.write( "The goal is to make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E+%3C=+0.7 ALIGN=MIDDLE  ALT=\"E+%3C=+0.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------<BR>\n" );
document.write( "----------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Final Answer: <font color=red>85</font><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );