document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109930>Question 1109930</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hirty percent of salespersons in ABC Ltd. are male. A random sample of 100<BR>\n" );
document.write( "salespersons is selected.<BR>\n" );
document.write( "(a) Which distribution does this scenario fit and why? <BR>\n" );
document.write( "(b) Define the variable of interest, X. <BR>\n" );
document.write( "(c) What are the possible values of X? <BR>\n" );
document.write( "(d) What is the expected number of males? <BR>\n" );
document.write( "(e) What is the standard deviation of the number of males? <BR>\n" );
document.write( "(f) What is the probability that there are exactly 25 males in the sample?\r<BR>\n" );
document.write( "\n" );
document.write( "(g) What is the probability of getting less than 36 males?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724907 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=724907\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a 1 sample proportion test<BR>\n" );
document.write( "x is the random variable and the proportion of those chosen who are male<BR>\n" );
document.write( "possible values are [0, 100], integers only.<BR>\n" );
document.write( "E(X)=np=0.3*100=30.<BR>\n" );
document.write( "V(X)=np(1-p)=30*0.7=21<BR>\n" );
document.write( "sd is sqrt (21) or 4.6<BR>\n" );
document.write( "probability of 24 males is 100C25*0.3^25*0.7^75=0.0496<BR>\n" );
document.write( "getting fewer than 36 using normal approximation at 35.5<BR>\n" );
document.write( "(35.5-30)/4.6 is z<BR>\n" );
document.write( "z=+1.20<BR>\n" );
document.write( "probability that z < 1.20 is 0.8849.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );