document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1020389>Question 1020389</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.Suppose we are flipping a fair coin (i.e., probability of heads = .5 and probability of tails = .5). What is the probability that in a sample of 5 flips, fewer than 4 will be heads?\r<BR>\n" );
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document.write( "2.The U.S. mint, which produces billions of coins annually, has a mean daily defect rate of 4 coins. Let X be the number of defective coins produced on a given day.\r<BR>\n" );
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document.write( "What is the variance of this distribution?\r<BR>\n" );
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document.write( "3. Consider the following discrete distribution. Note that x represents the value of a particular outcome and P(x) represents the probability of that outcome.\r<BR>\n" );
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document.write( "x	P(x)<BR>\n" );
document.write( "0	0.1<BR>\n" );
document.write( "1	0.2<BR>\n" );
document.write( "2	0.3<BR>\n" );
document.write( "3	0.2<BR>\n" );
document.write( "4	0.1<BR>\n" );
document.write( "5	0.1<BR>\n" );
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document.write( "What is the probability that an observed x is less than or equal to 3? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #636309 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=636309\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. The statistical experiment follows the binomial distribution, with pmf <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29+=+C%285%2Cx%29%2A0.5%5E%285-x%290.5%5Ex+=+C%285%2Cx%290.5%5E5 ALIGN=MIDDLE  ALT=\"p%28x%29+=+C%285%2Cx%29%2A0.5%5E%285-x%290.5%5Ex+=+C%285%2Cx%290.5%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The answer is p(0) + p(1) + p(2) + p(3).  But an easier way is to evaluate 1-p(4)-p(5) = 1-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C%285%2C4%29%2BC%285%2C5%29%29%2A0.5%5E5+=+6%2A0.5%5E5 ALIGN=MIDDLE  ALT=\"%28C%285%2C4%29%2BC%285%2C5%29%29%2A0.5%5E5+=+6%2A0.5%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1-3/16 = 13/16 = 0.8125.\r<BR>\n" );
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document.write( "3.  The answer is p(0) + p(1) + p(2) + p(3), but it is easier to compute 1- p(4)-p(5) = 1-0.1 - 0.1 = 0.8. </SPAN>\n" );
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