document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1073291>Question 1073291</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Based on historical data, your manager believes that 34% of the company's orders come from first-time customers. A random sample of 113 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is greater than than 0.15?\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688122 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=688122\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Can use the normal approximation to this binomial.<BR>\n" );
document.write( "np=mean which historically would be 38.42<BR>\n" );
document.write( "np(1-p) is variance or 25.3572; sqrt is sd=5.036<BR>\n" );
document.write( "a proportion of 0.15 represents 16.95<BR>\n" );
document.write( "So z>=(16.95-38.42)/5.036=-4.26, which is about 100%.<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "z>(0.15-0.34)/sqrt((0.34*0.66)/113)=-0.19/0.0446, which is z>-4.26 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );