document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183155>Question 1183155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> According to a survey, only 15% of customers who visited the website of a major retail store made a purchase. Random samples of size 50 are selected. What proportion of the samples will have less than 15% of customers who will make a purchase after visiting the website? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813680 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=813680\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is asking what proportion of samples of 50 will have 7 or fewer customers who made a purchase?<BR>\n" );
document.write( "that is asking what is the probability that with a 15% base rate 0.14 or fewer will make a purchase?<BR>\n" );
document.write( "this is z=(0.14-0.15)/sqrt(0.15*0.85/50)<BR>\n" );
document.write( "< -0.01/0.0505<BR>\n" );
document.write( "< -0.1980<BR>\n" );
document.write( "That probability is 0.4215<BR>\n" );
document.write( "-<BR>\n" );
document.write( "Can use a normal approximation as a rough check.<BR>\n" );
document.write( "mean is np=7.5<BR>\n" );
document.write( "variance is np(1-p)=6.375<BR>\n" );
document.write( "sd is sqrt (V)=2.525<BR>\n" );
document.write( "and get a similar result.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );