document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=929314>Question 929314</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Compute P(X) using the binomial probability formula.  Then determine whether the normal distribution can be used to estimate this probability.  If so, approximate P(X) using the normal distribution and compare the result with the exact probability. \r<BR>\n" );
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document.write( "n=58<BR>\n" );
document.write( "p=0.3<BR>\n" );
document.write( "x=12\r<BR>\n" );
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document.write( "ANSWER A, B, AND C BELOW. \r<BR>\n" );
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document.write( "a) For n=58, p= 0.3, and x=12, use the binomial probability formula to find P(X).\r<BR>\n" );
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document.write( "b) Approxiamte P(x) using the normal distribution.  Use a standard distribution table.\r<BR>\n" );
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document.write( "c)By how much to the probabilities differ?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #564203 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=564203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  n=58, p= 0.3, q = .7<BR>\n" );
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document.write( "a) P(x=12) = 58C12(.3)^12(.7)^46  0r  P(x=12) = binompdf(58, .3,12) = .0355<BR>\n" );
document.write( "b) normal distribution can be used to estimate this probability: both np  and nq  &#8805;  5<BR>\n" );
document.write( ".........<BR>\n" );
document.write( "Using a Casio fx-115 ES plus<BR>\n" );
document.write( "mean = .3•58 = 17.4,  s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28.3%2A.7%2A58%29 ALIGN=MIDDLE  ALT=\"sqrt%28.3%2A.7%2A58%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3.49<BR>\n" );
document.write( "P(x = 12) = normalpdf(12, 3.49, 17.4) = .0345 <BR>\n" );
document.write( "....<BR>\n" );
document.write( "c) .0355 - .0345 = .0010, the amount the probabilities differ<BR>\n" );
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