document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081891>Question 1081891</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Recall that for use of a normal distribution as an approximation to the binomial distribution, the conditions np > 5 and nq > 5 must be met. For p = 0.2, compute the minimum sample size needed for use of the normal approximation. Round to the nearest whole number.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695930 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=695930\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Plug p = 0.2 into the first inequality and solve for n\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Ap+%3E+5 ALIGN=MIDDLE  ALT=\"n%2Ap+%3E+5\"   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=n+%3E+25 ALIGN=MIDDLE  ALT=\"n+%3E+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For the second inequality plug q = 1-p in first, then plug in p = 0.2, and solve for n\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2A%281-p%29+%3E+5 ALIGN=MIDDLE  ALT=\"n%2A%281-p%29+%3E+5\"   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=n%2A0.8+%3E+5 ALIGN=MIDDLE  ALT=\"n%2A0.8+%3E+5\"   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=n+%3E+6.25 ALIGN=MIDDLE  ALT=\"n+%3E+6.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Intersecting the two inequalities <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%3E+25 ALIGN=MIDDLE  ALT=\"n+%3E+25\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%3E+6.25 ALIGN=MIDDLE  ALT=\"n+%3E+6.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > leads to just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%3E+25 ALIGN=MIDDLE  ALT=\"n+%3E+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, as this is the region they both share in common\r<BR>\n" );
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document.write( "So overall, the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%3E+25 ALIGN=MIDDLE  ALT=\"n+%3E+25\"   DISABLED_style= \"max-width:90%; height:auto;\" > where n is a positive whole number.\r<BR>\n" );
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document.write( "We'll need n to be larger than 25 in order to use a normal approximation.\r<BR>\n" );
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document.write( "<font size=4 color=red>The min sample size needed is 26</font>  </SPAN>\n" );
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