document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081734>Question 1081734</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A simple random sample of size n=15 is obtained from a population with &#956;=66 and &#963;=14.\r<BR>\n" );
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document.write( "&#8203;(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample&#8203; mean? Assuming that this condition is&#8203; true, describe the sampling distribution of overbarx.\r<BR>\n" );
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document.write( "&#8203;(b) Assuming the normal model can be&#8203; used, determine &#8203;P(overbar x < 69.5&#8203;).\r<BR>\n" );
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document.write( "&#8203;(c) Assuming the normal model can be&#8203; used, determine &#8203;P(overbar x &#8805; 67.6&#8203;).<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 #695780 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=695780\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the population must be treated as normally distributed or close to it, given that a sample is being taken that is relatively small.<BR>\n" );
document.write( "the sampling distribution is then N~(66, 14/sqrt(10))<BR>\n" );
document.write( "probability mean is  < 69.5 in the sample is z<(69.5-66)/(14/sqrt(10))<BR>\n" );
document.write( "=3.5*sqrt(10)/14=0.7906<BR>\n" );
document.write( "probability z < 0.79 is 0.7852<BR>\n" );
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document.write( "z>=(67.6-66)*sqrt(10)/14<BR>\n" );
document.write( "z>0.36<BR>\n" );
document.write( "probability is 0.3594 </SPAN>\n" );
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