document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1075146>Question 1075146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> John parks cars at a hotel. On the average, 6.7 cars will arrive in an hour. Assume that a driver's<BR>\n" );
document.write( "decision on whether to let John park the car does not depend upon any other person's decision.<BR>\n" );
document.write( "Define the random variable x to be the number of cars arriving in any hour period.<BR>\n" );
document.write( "a. What is the appropriate probability distribution for x? Explain how x satisfies the<BR>\n" );
document.write( "properties of the distribution.<BR>\n" );
document.write( "b. Compute the probability that exactly 5 cars will arrive in the next hour.<BR>\n" );
document.write( "c. Compute the probability that no more than 5 cars will arrive in the next hour </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #689857 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=689857\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Random, numbers proportional to time, discrete, could be theoretically infinite.<BR>\n" );
document.write( "Poisson distribution with parameter 6.7<BR>\n" );
document.write( "P(x)=exp^(-6.7)*6.7^x/x! for x between 0 and infinity.<BR>\n" );
document.write( "P(5)=e^-6.7*6.7^5/5!=0.1385<BR>\n" );
document.write( "no more than 5<BR>\n" );
document.write( "do 0-4<BR>\n" );
document.write( "for 0 it is 0.0012<BR>\n" );
document.write( "for 1 it is 0.0082<BR>\n" );
document.write( "for 2 it is 0.0276<BR>\n" );
document.write( "for 3 it is 0.0617<BR>\n" );
document.write( "for 4 it is 0.1034<BR>\n" );
document.write( "The sum of the 6 values is 0.3406. ANSWER<BR>\n" );
document.write( "This makes sense. The expected value is 6.7.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );