document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=615019>Question 615019</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me answer the following:<BR>\n" );
document.write( "(A) Find the binomial probability P(x = 4), where n = 12 and p = 0.40.<BR>\n" );
document.write( "(B) Set up, without solving, the binomial probability P(x is at most 4) using probability notation.<BR>\n" );
document.write( "(C) How would you find the normal approximation to the binomial probability P(x = 4) 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 #386863 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=386863\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (A) Find the binomial probability P(x = 4), where n = 12 and p = 0.40.<BR>\n" );
document.write( "P(x=4) = 12C4*0.4^4*0.6^8 = 0.2128<BR>\n" );
document.write( "-------------------------------------------------<BR>\n" );
document.write( "(B) Set up, without solving, the binomial probability P(x is at most 4) using probability notation.<BR>\n" );
document.write( "P(0<= x <=4) = 12C0*0.4^0*0.6^12 + 12C1*0.4*0.6^11+...+12C4*0.4^4*0.6^8<BR>\n" );
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document.write( "(C) How would you find the normal approximation to the binomial probability P(x = 4) in part A? <BR>\n" );
document.write( "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.<BR>\n" );
document.write( "u = np = 0.4*12 = 4.8<BR>\n" );
document.write( "s = sqrt(npq) = sqrt(4.8*0.6) = 1.6971<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Normal approx: P(3.5< x < 4.5)<BR>\n" );
document.write( "z(3.5) = (3.5-4.8)/1.6971<BR>\n" );
document.write( "z(4.5) = (4.5-4.8)/1.6871<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P(z(3.5)<= z <z(4.5)) is the approximation.<BR>\n" );
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document.write( "cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "================= <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );