document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195851>Question 1195851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Historically, 93% of the deliveries of an overnight mail service arrive before 10:30 the following morning. If a random sample of 500 deliveries is selected, what is the probability the sample will have more than 95% of the deliveries arriving before 10:30 the following morning? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828469 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=828469\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is calculating a z-value which is here z=(phat-p)/sqrt (p*(1-p)/n)<BR>\n" );
document.write( "=0.02/sqrt(0.93*0.07/500)\r<BR>\n" );
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document.write( "=0.02/0.0114<BR>\n" );
document.write( "=1.75<BR>\n" );
document.write( "Probability z > 1.75 is 0.0398<BR>\n" );
document.write( "-<BR>\n" );
document.write( "Can check with a normal approximation<BR>\n" );
document.write( "mean is 0.93*500=465<BR>\n" );
document.write( "variance is that *0.07=32.55<BR>\n" );
document.write( "sd is sqrt of that=5.71<BR>\n" );
document.write( "95% of 500 is 475<BR>\n" );
document.write( "so z=(475.5-465)/5.71, using the continuity correction factor<BR>\n" );
document.write( "=1.84 and the probability of z> 1.84 is 0.0329.   </SPAN>\n" );
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