document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192814>Question 1192814</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A normal population has a mean of $67 and standard deviation of $19. You select random samples of nine.\r<BR>\n" );
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document.write( "a.What is the standard error of the sampling distribution of sample means?\r<BR>\n" );
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document.write( "b.What is the probability that a sample mean is greater than $70?\r<BR>\n" );
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document.write( "c.What is the probability that a sample mean is less than $63?\r<BR>\n" );
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document.write( "d. What is the probability that a sample mean is between $63 and $70?\r<BR>\n" );
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document.write( "e.What is the probability that the sampling error (  x⎯⎯  − μ) would be $9 or more? That is, what is the probability that the estimate of the population mean is less than $58 or more than $76? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824720 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=824720\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It is $19/sqrt(9), the sd/sqrt(n)=$6.33<BR>\n" );
document.write( "b. z=(x-mean)/sigma/sqrt(n)=3/(19/3)=0.4739<BR>\n" );
document.write( "prob. z >0.4739=0.3178<BR>\n" );
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document.write( "c. This is z <-4/6.33 =-0.6319; probability of that is 0.2637<BR>\n" );
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document.write( "d.Between 63 and 70 is 1- the sum of those two probabilities above, or 1-0.5815=0.4185<BR>\n" );
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document.write( "e. This would be +/- 9/6.33=1.42. That probability is 1-0.8444 (the probability between them)=0.1556.<BR>\n" );
document.write( "There will be slight differences in the fourth decimal place if you round the z-value. Generally, 2 places may be done, but some may want you to round the z-value only at the end. </SPAN>\n" );
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