document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=523347>Question 523347</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A basketball team's star 3-point shooter takes six 3- point shots in a game. Historically, he makes 40% of all 3-point shots taken in a game. State at the outset what assumptions you have made.\r<BR>\n" );
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document.write( "(a) Find the probability that at least two shots were made.<BR>\n" );
document.write( "(b) Find the probability that exactly three shots were made.<BR>\n" );
document.write( "(c) Find the mean and standard deviation of the num¬ber of shots made.<BR>\n" );
document.write( "(d) Find the mean and standard deviation of the total number of points scored as a result of these shots.<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 #347300 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=347300\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A basketball team's star 3-point shooter takes six 3- point shots in a game. Historically, he makes 40% of all 3-point shots taken in a game. State at the outset what assumptions you have made.<BR>\n" );
document.write( "Independent trials; binomial results;<BR>\n" );
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document.write( "(a) Find the probability that at least two shots were made.<BR>\n" );
document.write( "P(2<= x <= 6) = 1 - binomcdf(6,0.4,1) = 0.7667<BR>\n" );
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document.write( "(b) Find the probability that exactly three shots were made.<BR>\n" );
document.write( "P(x = 3) = 6C3*0.4^3*0.6^3 = 0.2765<BR>\n" );
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document.write( "(c) Find the mean and standard deviation of the num¬ber of shots made.<BR>\n" );
document.write( "mean = np = 6*0.4 = 2.4<BR>\n" );
document.write( "std = sqrt(npq) = sqrt(2.4*0.6) = 1.2<BR>\n" );
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document.write( "(d) Find the mean and standard deviation of the total number of points scored as a result of these shots.<BR>\n" );
document.write( "mean # of points: 2.4*3 = 7.2<BR>\n" );
document.write( "std of # of points: 1.2*3 = 3.6<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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