document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151047>Question 1151047</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the number of students in a class for the Business Statistics program at a University has a mean of 23 with a standard deviation of 4.3. If 15 classes are selected randomly, find the probability that the mean number of students is between 20 and 30. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #772669 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=772669\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu ALIGN=MIDDLE  ALT=\"mu\"   DISABLED_style= \"max-width:90%; height:auto;\" > = mu = greek letter representing the population mean<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma ALIGN=MIDDLE  ALT=\"sigma\"   DISABLED_style= \"max-width:90%; height:auto;\" > = sigma = greek letter representing the population standard deviation<BR>\n" );
document.write( "n = sample size<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \overline{x}\"> = xbar = sample mean\r<BR>\n" );
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document.write( "In this case,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+23 ALIGN=MIDDLE  ALT=\"mu+=+23\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma+=+4.3 ALIGN=MIDDLE  ALT=\"sigma+=+4.3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+15 ALIGN=MIDDLE  ALT=\"n+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We're given two xbar values which are 20 and 30\r<BR>\n" );
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document.write( "Compute the z score for the raw score xbar = 20<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28xbar+-+mu%29%2F%28sigma%2Fsqrt%28n%29%29 ALIGN=MIDDLE  ALT=\"z+=+%28xbar+-+mu%29%2F%28sigma%2Fsqrt%28n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%2820+-+23%29%2F%284.3%2Fsqrt%2815%29%29 ALIGN=MIDDLE  ALT=\"z+=+%2820+-+23%29%2F%284.3%2Fsqrt%2815%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+-2.702081 ALIGN=MIDDLE  ALT=\"z+=+-2.702081\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+-2.70 ALIGN=MIDDLE  ALT=\"z+=+-2.70\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Repeat for xbar = 30<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28xbar+-+mu%29%2F%28sigma%2Fsqrt%28n%29%29 ALIGN=MIDDLE  ALT=\"z+=+%28xbar+-+mu%29%2F%28sigma%2Fsqrt%28n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%2830+-+23%29%2F%284.3%2Fsqrt%2815%29%29 ALIGN=MIDDLE  ALT=\"z+=+%2830+-+23%29%2F%284.3%2Fsqrt%2815%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+6.304856 ALIGN=MIDDLE  ALT=\"z+=+6.304856\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+6.30 ALIGN=MIDDLE  ALT=\"z+=+6.30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE P\left(20 < \overline{x} < 30\right) \approx P\left(-2.70 < Z < 6.30\right)\">\r<BR>\n" );
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document.write( "Use a Z table such as this one<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.z-table.com/\">http://www.z-table.com/</a><BR>\n" );
document.write( "to find that,<BR>\n" );
document.write( "P(Z < -2.70) = 0.0035<BR>\n" );
document.write( "P(Z < 6.30) = 1.00<BR>\n" );
document.write( "note: if k is larger than 3.4, then P(Z < k) will be very very close to 1.00; this is especially true of z = 6.30 as its very distant from the center z = 0. So that is how I got P(Z < 6.30) = 1.00\r<BR>\n" );
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document.write( "Subtract the values to find the area between the z scores<BR>\n" );
document.write( "P(A < Z < B) = P(Z < B) - P(Z < A)<BR>\n" );
document.write( "P(-2.70 < Z < 6.30) = P(Z < 6.30) - P(Z < -2.70)<BR>\n" );
document.write( "P(-2.70 < Z < 6.30) = 1 - 0.0035<BR>\n" );
document.write( "P(-2.70 < Z < 6.30) = 0.9965\r<BR>\n" );
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document.write( "<font color=red size=4>Answer: 0.9965</font><BR>\n" );
document.write( "This answer is approximate.\r<BR>\n" );
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document.write( "side note:<BR>\n" );
document.write( "You can use a calculator like this one<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\">http://davidmlane.com/hyperstat/z_table.html</a><BR>\n" );
document.write( "to compute the area under the Z curve. Leave the mean and standard deviation as 0 and 1 respectively. Click the \"between\" radio button and type in the values -2.70 and 6.30 into the boxes. Then hit \"recalculate\" to have the answer come up. This can also be done on TI83 and TI84 calculators as well using the normalcdf function.<BR>\n" );
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