document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=223170>Question 223170</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A light bulb manufacturer claims his light bulbs will last 500 hours on the average. The lifetime of a light bulb is assumed to follow an exponential distribution.<BR>\n" );
document.write( "a.	What is the probability that the light bulb will have to replaced within 500 hours?<BR>\n" );
document.write( "b.	What is the probability that the light bulb will last more than 1000 hours?<BR>\n" );
document.write( "c.	What is the probability that the light bulb will last between 200 and 800 hours?<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 #167041 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=167041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A light bulb manufacturer claims his light bulbs will last 500 hours on the average. The lifetime of a light bulb is assumed to follow an exponential distribution.<BR>\n" );
document.write( "a.	What is the probability that the light bulb will have to replaced within 500 hours?<BR>\n" );
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document.write( "lamda = 1/500<BR>\n" );
document.write( "Ans: P(x<=500) = 1 - e^(-lamda*x) = 1-e^[(-1/500)*500] = 1-e^-1 = 0.6321\r<BR>\n" );
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document.write( "b.	What is the probability that the light bulb will last more than 1000 hours?<BR>\n" );
document.write( "Ans:P(x>=1000) =  1 - P(x<=1000) = 1 -[1-e^(-1/500*1000)<BR>\n" );
document.write( "= 1 -[1-e^(-2)] = e^(-2) = 0.1353<BR>\n" );
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document.write( "c.	What is the probability that the light bulb will last between 200 and 800 hours?<BR>\n" );
document.write( "Answer will be P(x<=800)-P(x<=200)<BR>\n" );
document.write( "Remember P(x<=k) = 1-e^(-lambda*k)<BR>\n" );
document.write( "I'll leave that to you.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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