document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1056997>Question 1056997</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5.92 The Challenger Disaster. In a letter to the editor that appeared in the February 23, 1987, issue of U.S. News and World Report, a reader discussed the issue of space-shuttle safety. Each “criticality 1” item must have a 99.99% reliability, by NASA standards, which means that the probability of failure for a “criticality1” item is only 0.0001. Mission 25, the mission in which the Challenger exploded on takeoff, had 748 “criticality 1” items.<BR>\n" );
document.write( "Use the Poisson approximation to the binomial distribution to determine the approximate probability that\r<BR>\n" );
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document.write( "   a. none of the “criticality 1” items would fail.<BR>\n" );
document.write( "   b. at least one “criticality 1” item would fail. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #672107 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=672107\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> n must be greater than or = 100, our n is 748<BR>\n" );
document.write( "Probability(Pr) must be less than or = 0.01, our Pr is 0.0001<BR>\n" );
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document.write( "our constant lambda is 748 * 0.0001 = 0.0748<BR>\n" );
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document.write( "a) Pr ( x = 0 ) = (e^(-0.0748) * 0.0748^0) / 0! = 0.9279<BR>\n" );
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document.write( "b) Pr ( x > or = 1 ) = 1 - Pr ( x = 0 ) = 1 - 0.9279 = 0.0721<BR>\n" );
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document.write( "Note that Dr Richard Feynman proved that by NASA's ignoring the advice of Morton Thiercol rocket engineers and the physics of cold on rubber seals they created a 100% chance of failure </SPAN>\n" );
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