document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=453899>Question 453899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help Please!\r<BR>\n" );
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document.write( "It has been estimated that with a sophisticated mathematical strategy, a player can increase the probability of winning at black jack to 10/19.  If you play with this strategy, what is the probability that you will win at least 8 games if you play 20?  (Use normal approximation)\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #311764 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=311764\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It has been estimated that with a sophisticated mathematical strategy, a player can increase the probability of winning at black jack to 10/19. If you play with this strategy, what is the probability that you will win at least 8 games if you play 20? (Use normal approximation)<BR>\n" );
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document.write( "mean = np = 20(10/19) = 10.526<BR>\n" );
document.write( "std = sqrt(npq) = sqrt[20(10/19)(9/19)] = 2.233<BR>\n" );
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document.write( "z(7.5) = (7.5-10.526)/2.233 = -1.355<BR>\n" );
document.write( "z(20.5) = (20.5-10.526)/2.233 = 4.467<BR>\n" );
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document.write( "P(8<= x <=20) = P(-1.355<= z <= 4.467) = 0.9123<BR>\n" );
document.write( "===============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
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