document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=861562>Question 861562</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3. Assume a binomial probability distribution has p = .60 and n = 200.<BR>\n" );
document.write( "a. What are the mean and standard deviation?<BR>\n" );
document.write( "b. Is this situation one in which binomial probabilities can be approximated by the normal probability distribution?<BR>\n" );
document.write( "c. What is the probability of 100 to 110 successes?<BR>\n" );
document.write( "d. What is the probability of 130 or more successes?<BR>\n" );
document.write( "e. What is the advantage of using the normal probability distribution to approximate the binomial probabilities? <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 #519129 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=519129\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume a binomial probability distribution has p = .60 and n = 200.<BR>\n" );
document.write( "a. What are the mean and standard deviation?<BR>\n" );
document.write( "mean = np = 200*0.6 = 120<BR>\n" );
document.write( "std: = sqrt(npq) =  sqrt(120*0.4) = sqrt(48) = 4sqrt(3)<BR>\n" );
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document.write( "b. Is this situation one in which binomial probabilities can be approximated by the normal probability distribution?<BR>\n" );
document.write( "Yes:: Both np and qp > 5<BR>\n" );
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document.write( "c. What is the probability of 100 to 110 successes?<BR>\n" );
document.write( "Find P(99.5 <= x <= 110.5)<BR>\n" );
document.write( "z(99.5) = (99.5-120)/sqrt(48) = -2.95<BR>\n" );
document.write( "z(110.5) = (110.5-120)/sqrt(48) = -1.37<BR>\n" );
document.write( "P(99.5<= x <=110.5) = P(-2.95<= z <=-1.37) = 0.0838<BR>\n" );
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document.write( "Use the same procedure on the next problem.\r<BR>\n" );
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document.write( "d. What is the probability of 130 or more successes?<BR>\n" );
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document.write( "e. What is the advantage of using the normal probability distribution to approximate the binomial probabilities?<BR>\n" );
document.write( "Check your textbook to discuss these advantages.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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