document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=433383>Question 433383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a local university, 40% of the students live in dormitories.  A random sample of n = 80 students is selected for a particular study.\r<BR>\n" );
document.write( "\n" );
document.write( "(a) What is the sampling distribution of P? Please provide its general shape, its standard deviation, and its mean. \r<BR>\n" );
document.write( "\n" );
document.write( "(b) What is the probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #300426 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=300426\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a local university, 40% of the students live in dormitories. A random sample of n = 80 students is selected for a particular study. <BR>\n" );
document.write( "(a) What is the sampling distribution of P?<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Note: You have not provided a description of P.<BR>\n" );
document.write( "Is it the proportions of all samples of size 80?<BR>\n" );
document.write( "Is it the <BR>\n" );
document.write( "----<BR>\n" );
document.write( "If it is the population:<BR>\n" );
document.write( "mean = np = 80*0.4 = 32<BR>\n" );
document.write( "std = sqrt(npq) = sqrt(32*0.6) = 4.3817..<BR>\n" );
document.write( "---------------------------------------------<BR>\n" );
document.write( "If it is the proportions of samples of size 80:<BR>\n" );
document.write( "mean =  0.4<BR>\n" );
document.write( "std = sqrt[0.4*0.6/80] = 0.0548<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( " Please provide its general shape, its standard deviation, and its mean.<BR>\n" );
document.write( "---- <BR>\n" );
document.write( "(b) What is the probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50?<BR>\n" );
document.write( "z(0.3) = (0.3-0.4)/0.0549 = -1.8215<BR>\n" );
document.write( "z(0.5) = (0.5-0.4)/0.0549 = 1.8215<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "P(0.3< x <0.5) = (-1.8215< x < 1.8215) = 0.9315<BR>\n" );
document.write( "===============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );