document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177992>Question 1177992</A>: <I><SPAN STYLE=\"word-break: break-all;\"> CNNBC recently reported that the mean annual cost of auto insurance is 1002 dollars. Assume the standard deviation is 278 dollars. You take a simple random sample of 76 auto insurance policies.\r<BR>\n" );
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document.write( "Find the probability that a single randomly selected value is less than 981 dollars.<BR>\n" );
document.write( "P(X < 981) = \r<BR>\n" );
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document.write( "Find the probability that a sample of size  <BR>\n" );
document.write( "n<BR>\n" );
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document.write( "76<BR>\n" );
document.write( "  is randomly selected with a mean less than 981 dollars.<BR>\n" );
document.write( "P(M < 981) = \r<BR>\n" );
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document.write( "Enter your answers as numbers accurate to 4 decimal places.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807159 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=807159\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(x<981); z=(x-mean)/sd; 981-1002=-21<BR>\n" );
document.write( "z < -21/278=-0.0755<BR>\n" );
document.write( "probability is 0.4699<BR>\n" );
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document.write( "sample mean <981 is z=(x bar-mean)/sigma/sqrt(n)<BR>\n" );
document.write( "z < (-21)/278/sqrt(76)<BR>\n" );
document.write( "=(-21/278)*(sqrt(76)/278=-0.6585<BR>\n" );
document.write( "probability z < -0.6585=0.2551\r<BR>\n" );
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document.write( "Much less likely that the mean of a sample of 76 will be as small as 981 or less.<BR>\n" );
document.write( "The fourth decimal place will change depending on the rules given for rounding z. If to two places, it will be different from the values here. </SPAN>\n" );
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