document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=617662>Question 617662</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me in answering the following:<BR>\n" );
document.write( "(A) Find the binomial probability P(x = 5), where n = 12 and p = 0.70.<BR>\n" );
document.write( "(B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation.<BR>\n" );
document.write( "(C) How would you find the normal approximation to the binomial probability P(x = 5) in part A? Please show how you would calculate µ and &#963; in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #388501 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=388501\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) Find the binomial probability P(x=5), where (n=13) and p=0.70.<BR>\n" );
document.write( "P(x=5) = 13C5(0.7)^5*0.3^8 = 0.0142<BR>\n" );
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document.write( "B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation.<BR>\n" );
document.write( "P(x >= 5) = 1 - P(0<= x <=4) = 1-0.0034 = 0.9966<BR>\n" );
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document.write( "C) How would you find the normal approximation to the binomial probability <BR>\n" );
document.write( "P(x=5) in part A? Please show how you would caculate u and o in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the caculations.<BR>\n" );
document.write( "u = np = 13*0.7 = 9.1<BR>\n" );
document.write( "sigma = sqrt(npq) = sqrt(9.1*0.3) = 1.6523<BR>\n" );
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document.write( "Switching from Binomial to Normal:<BR>\n" );
document.write( "P(x = 5) = P(4.5 <= x <= 5.5)<BR>\n" );
document.write( "z(4.5) = (4.5-9.1)/1.6523 = -2.7840<BR>\n" );
document.write( "z(5.5) = (5.5-9.1)/1.6523 = -2.1788<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "P(4.5 <= x <= 5.5) = P(-2.7840<= z <= -2.1788) = 0.0120<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=============\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );