document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133709>Question 1133709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> CNNBC recently reported that the mean annual cost of auto insurance is 1016 dollars. Assume the standard deviation is 268 dollars. You take a simple random sample of 61 auto insurance policies.\r<BR>\n" );
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document.write( "1. Find the probability that a single randomly selected value is less than 990 dollars. <BR>\n" );
document.write( "P(X < 990) = ____________(Enter your answers as numbers accurate to 4 decimal places)\r<BR>\n" );
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document.write( "2. Find the probability that a sample of size <BR>\n" );
document.write( "n= 61 is randomly selected with a mean less than 990 dollars. <BR>\n" );
document.write( "P(M < 990) = __________(Enter your answer 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 #750953 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=750953\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. z<=(x-mean)/sd or <=(990-1016)/268 or -26/268 or -0.10. Assume the sd is known as a population since the sample sd is not given.<BR>\n" );
document.write( "probability z is less than that is 0.4602\r<BR>\n" );
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document.write( "2. z<=(x-mean)/sigma/sqrt(n), assuming the sd is known as a population.<BR>\n" );
document.write( "z<=(990-1016)/268/sqrt(61)<BR>\n" );
document.write( "z<=(-26*sqrt(61))/268 or -0.76. I use z to two decimal places<BR>\n" );
document.write( "that probability is 0.2236 </SPAN>\n" );
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