document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160699>Question 1160699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A production run is not acceptable for shipment to customers if a sample of 100 items<BR>\n" );
document.write( "contains 5% or more defective items. If a production run has a population proportion<BR>\n" );
document.write( "defective of P  0.100 , what is the probability that P will be at least 0.05?<BR>\n" );
document.write( "(a) In an effort to estimate the mean amount spent per customer for dinner at a major<BR>\n" );
document.write( "restaurant, data were collected for a sample of 49 customers over a three-week<BR>\n" );
document.write( "period.<BR>\n" );
document.write( "(i) Assume a population standard deviation of $10, 000. What is the standard<BR>\n" );
document.write( "error of the mean?<BR>\n" );
document.write( "(ii) With a .95 probability, what statement can be made about the sampling<BR>\n" );
document.write( "error?<BR>\n" );
document.write( "(iii) If the sample mean is $90, 400, what is the 95% confidence interval for<BR>\n" );
document.write( "population mean? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784085 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=784085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Have a high enough np for normal approximation,<BR>\n" );
document.write( "the mean for the population is np=10 defective<BR>\n" );
document.write( "the variance is np(1-p)=9<BR>\n" );
document.write( "sd is sqrt(V)=3<BR>\n" );
document.write( "probability >=5 (in other words 0.05 probability for that group) is z > (4.5-10)/3=-1.83 for probability 0.9664\r<BR>\n" );
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document.write( "exact would be probability for 0-4 given n=100 and p=0.1, and taking the complement of that answer, which is  0.0237, so 1-0.0237=0.9763.\r<BR>\n" );
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document.write( "SEM is s/sqrt(n)=10000/7=$1428.57<BR>\n" );
document.write( "CI 95%: half-interval is t0.975, df=48)=2.01*s/sqrt(n)=$2872.28<BR>\n" );
document.write( "the CI is mean +/- the half-interval<BR>\n" );
document.write( "=($87,528, $93,272)\r<BR>\n" );
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document.write( "The sampling error is approximately $2872.<BR>\n" );
document.write( "We are 95% confident that the population mean is in the above interval.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );