document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=387293>Question 387293</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A distribution of scores has µ = 40 and &#963; = 18<BR>\n" );
document.write( "a. describe the distribution of sample means based on samples of n = 36 selected from this population (shape, central tendency, variability) <BR>\n" );
document.write( "b. of all the possible samples of n = 36, what proportion will have sample means greater than 43?<BR>\n" );
document.write( "c. of all the possible samples of n = 36, what proportion will have sample means less than 34?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #273781 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=273781\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a.  n = 36, this is considered a large sample.  For large samples, the Central Limit Theorem says that the distribution of the sample means is approximately normal (getting better as n gets higher and higher).  The mean is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+40 ALIGN=MIDDLE  ALT=\"mu+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" >and the variance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28sigma%29_X%29%5E2+=+sigma%5E2%2Fn ALIGN=MIDDLE  ALT=\"%28%28sigma%29_X%29%5E2+=+sigma%5E2%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "b.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X+%3E+43%29+=+P%28%28X+-+40%29%2F%2818%2Fsqrt%2836%29%29+%3E+%2843+-+40%29%2F3+=+1%29 ALIGN=MIDDLE  ALT=\"P%28X+%3E+43%29+=+P%28%28X+-+40%29%2F%2818%2Fsqrt%2836%29%29+%3E+%2843+-+40%29%2F3+=+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X+%3E+43%29+=+P%28Z+%3E+1%29+=+0.1587 ALIGN=MIDDLE  ALT=\"P%28X+%3E+43%29+=+P%28Z+%3E+1%29+=+0.1587\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "c. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X+%3C+34%29+=+P%28%28X+-+40%29%2F%2818%2Fsqrt%2836%29%29%3E+%2834+-+40%29%2F3+=+-2%29 ALIGN=MIDDLE  ALT=\"P%28X+%3C+34%29+=+P%28%28X+-+40%29%2F%2818%2Fsqrt%2836%29%29%3E+%2834+-+40%29%2F3+=+-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X+%3C+34%29+=+P%28Z+%3C+-2%29+=+0.0228 ALIGN=MIDDLE  ALT=\"P%28X+%3C+34%29+=+P%28Z+%3C+-2%29+=+0.0228\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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