document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194452>Question 1194452</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In many situations, the normal distribution can be used to approximate the binomial distribution.<BR>\n" );
document.write( "a)Explain the conditions in which this can be done, and explain why we might take advantage of this property.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826656 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=826656\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If there are two outcomes with constant probability<BR>\n" );
document.write( "if np and n(1-p) are > 5 (some use 10)<BR>\n" );
document.write( "Do this where large factorials might occur and cannot be calculated.<BR>\n" );
document.write( "A batter is hitting 0.400. In the next 200 at bats, what is the chance of his getting 90 or more hits.<BR>\n" );
document.write( "With the binomial, this is 200C50 *0.4^90*0.6^110, and that is only for 90 hits. One has to calculate 91, 92,<BR>\n" );
document.write( "Normal approximation np=80 (mean)<BR>\n" );
document.write( "np(1-p)=80*0.6=48 (variance)<BR>\n" );
document.write( "sqrt 48 is 6.93<BR>\n" );
document.write( "want z>(89.5-80)/6.83, and that is a lot easier to do. </SPAN>\n" );
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