document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121297>Question 1121297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A commercial jet aircraft has four engines. For an aircraft in flight to land safely, at least two engines should be in working condition. Each engine has an independent reliability of p=92%.<BR>\n" );
document.write( "a) if the probability of landing safely must be at least 99.5% what is the minimum value for p ?<BR>\n" );
document.write( "b)...<BR>\n" );
document.write( "c)...<BR>\n" );
document.write( "The question is quoted from the book \"Complete Business Statistics\" 7th Edition by Sounderpandian (Asian edition)<BR>\n" );
document.write( "Chapter 3, problem 3-41 (page no.134) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #737135 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=737135\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it looks like 89% reliability is the magic number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that will give you an overall probability of 2 or more engines working at the same time of .995115.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "anything less than that will result in an overall probability of less than .995.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i used the binomial theorem and kept dropping the individual reliability percent down by 1 until the overall probability became less than 99.5%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in other words, i started at p = .92, then .91, then .90, then .89, then .88.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".89 was above 99.5% overall.<BR>\n" );
document.write( ".88 was below 99.5% overall.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the calculations are shown in the following spreadsheet printouts.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/081403.jpg\" alt=\"$$$\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/081404.jpg\" alt=\"$$$\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/081405.jpg\" alt=\"$$$\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i'm not exactly sure if this is the right formula to use, but if it is, there's a high probability that the answer will be correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the binomial formula tells you the probability of x occurrences out of n, given the probability that the event will occur or not occur.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula is p(x) = p^x * q^(n-x) * c(n,x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n is 4 in this problem.<BR>\n" );
document.write( "x ranges from 0 to 4.<BR>\n" );
document.write( "p is .92 or .91 or .90 or .89 or .88<BR>\n" );
document.write( "q is 1 - p<BR>\n" );
document.write( "c(n,x) is the numbe of ways you can get sets of x elements out of a set of n elements when order is not important.<BR>\n" );
document.write( "that formula is c(n,x) = n! / (x! * (n-x)!)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );