document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=333028>Question 333028</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1143 were positive.<BR>\n" );
document.write( "A. Construct a 95% confidence interval for the population proportion of positive drug tests.<BR>\n" );
document.write( "B. Why is the normality assumption not a problem, despite the very small value of p? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #238650 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=238650\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. compute the sample point estimate Pbar = 1143/86991 = 0.0131<BR>\n" );
document.write( "2. compute the standard error:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28pbar%2A%281-pbar%29%2Fn%29=sqrt%280.0131%2A%281-0.0131%29%2F86991%29=0.000386 ALIGN=MIDDLE  ALT=\"sqrt%28pbar%2A%281-pbar%29%2Fn%29=sqrt%280.0131%2A%281-0.0131%29%2F86991%29=0.000386\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3. Identify the critical value for 95% confidence:  Z=1.96<BR>\n" );
document.write( "4. Compute the 95% confidence interval for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi=population_proportion ALIGN=MIDDLE  ALT=\"pi=population_proportion\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   pbar -\+ Z*Standard Error = 0.0131-1.96*0.000386, 0.0131+1.96*0.000386<BR>\n" );
document.write( "   (0.0123, 0.0139)<BR>\n" );
document.write( "==<BR>\n" );
document.write( "Note:  This is a binomial distribution problem <BR>\n" );
document.write( "X = number testing positive~Binomial (n,p)=binomial(86991,0.0131)<BR>\n" );
document.write( "But since the sample size is large and n*pbar=1143 exceeds 10<BR>\n" );
document.write( "this meets the criteria for using the normal approximation to the Binomial. <BR>\n" );
document.write( "--<BR>\n" );
document.write( "This is needed since the Binomial is skewed in the extremes and these requirements limit the Binomial from the extremes, allowing the Normal approximation. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );