document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133983>Question 1133983</A>: <I><SPAN STYLE=\"word-break: break-all;\"> CNNBC recently reported that the mean annual cost of auto insurance is 1040 dollars. Assume the standard deviation is 293 dollars. You take a simple random sample of 84 auto insurance policies.\r<BR>\n" );
document.write( "\n" );
document.write( "(a) Find the probability that a single randomly selected value is less than 994 dollars. <BR>\n" );
document.write( "P(X < 994) = \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(b) Find the probability that a sample of size n=84 is randomly selected with a mean less than 994 dollars. <BR>\n" );
document.write( "P(M < 994) = \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Enter your answers as numbers accurate to 4 decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751245 by </B><A HREF=/tutors/aboutme.mpl?userid=Glaviolette><B>Glaviolette(140)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Glaviolette><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=Glaviolette><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=751245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am assuming the data is normally distributed.  If so, z scores can be used to solve.  Otherwise, I don't believe the problem can be solved.  \r<BR>\n" );
document.write( "\n" );
document.write( "a.  z = (994 - 1040)/293 = -.16<BR>\n" );
document.write( "Using a z-score table P(X < 994) = .4364\r<BR>\n" );
document.write( "\n" );
document.write( "b.  z = (994 - 1040)/(293/sq rt 84) = -1.44<BR>\n" );
document.write( "Using a z-score table M(X < 994) = .0749 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );