document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1020364>Question 1020364</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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( "On a given day, what is the probability of 3 or fewer defective coins<BR>\n" );
document.write( "On a given day, what is the probability of more than 3 defective coins?<BR>\n" );
document.write( "On a given day, what is the probability of exactly 4 defective coins<BR>\n" );
document.write( "what is the variance?\r<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 #636258 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=636258\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is an example of a rare event, so the Poisson distribution is the most appropriate to use.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29+=+%28mu%5Ex%2Fx%21%29%2Ae%5E%28-mu%29 ALIGN=MIDDLE  ALT=\"p%28x%29+=+%28mu%5Ex%2Fx%21%29%2Ae%5E%28-mu%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu ALIGN=MIDDLE  ALT=\"mu\"   DISABLED_style= \"max-width:90%; height:auto;\" > in this case is equal to 4.\r<BR>\n" );
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document.write( "==>The probability of 3 or fewer defective coins would be p(0) +p(1) + p(2) + p(3) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284%5E0%2F0%21%29%2B%284%5E1%2F1%21%29%2B%284%5E2%2F2%21%29%2B%284%5E3%2F3%21%29%29+%2Ae%5E%28-4%29+=+0.43347 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, to 5 decimal places.\r<BR>\n" );
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document.write( "==> The probability of more than 3 defective coins is 1 -  0.43347 = 0.56653.\r<BR>\n" );
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document.write( "The probability of exactly 4 defectives is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%284%29+=++%284%5E4%2F4%21%29%2Ae%5E%28-4%29=0.19537 ALIGN=MIDDLE  ALT=\"p%284%29+=++%284%5E4%2F4%21%29%2Ae%5E%28-4%29=0.19537\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to 5 decimal places.\r<BR>\n" );
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document.write( "For the Poisson distribution, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+sigma%5E2+=+4 ALIGN=MIDDLE  ALT=\"mu+=+sigma%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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