document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173159>Question 1173159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that on a highway, an average of four accidents occur per day.<BR>\n" );
document.write( "a) State the parameter for this probability distribution.<BR>\n" );
document.write( "b) Calculate the mean and standard deviation for this probability distribution.<BR>\n" );
document.write( "c) What is the probability that an accident will occur on a particular day?<BR>\n" );
document.write( "d) Find the probability that from 4 to 6 accidents will occur from 1:00pm to 7:00pm on a particular day.<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 #798416 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=798416\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a Poisson distribution- counts, proportional to time, could theoretically be infinite.<BR>\n" );
document.write( "Parameter is 4.<BR>\n" );
document.write( "Mean is 4 accidents a day, variance is 4 acc^2/day^2 and SD is 2 accidents/day<BR>\n" );
document.write( "that is 1-probability no accidents occurs on a day. The latter is e^(-4) or 0.0183, so the answer is 1-0.0183 or 0.9817.<BR>\n" );
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document.write( "A 6 hour period would be expected to have 1 accident during that time, since it is 1/4 of a day so 1/4 of 4 accidents is 1.<BR>\n" );
document.write( "Instead of e^(-4)*4^k/k! we have scaled it down to 1/4 of that so the distribution is e^(-1)*1^k/k!<BR>\n" );
document.write( "p(4)=e^(-1)1^4/4!=0.0153<BR>\n" );
document.write( "p(5)=e^(-1)*1^5/120=0.0031<BR>\n" );
document.write( "p(6)=0.0005 (the denominator is 6! or 720.<BR>\n" );
document.write( "The overall probability is 0.0189.<BR>\n" );
document.write( "This would be low probability, because one would be expecting the usual number of daily accidents to occur in 1/4 of the time.<BR>\n" );
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