document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=898153>Question 898153</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . Assuming that a plane makes a safe flight if at least half the numbers of engine run. Find whether a 6 engine plane or a 4 engine plane has a higher probability of successful flight. <BR>\n" );
document.write( "ii)	The marks obtained in Probability & Statistics by 1000 students is normally distributed is normally distributed with mean 78% and standard deviation 11%. Determine (a). How many students got the marks above 90%<BR>\n" );
document.write( "(b).What was the highest mark obtained by the lowest of 10% of the students <BR>\n" );
document.write( "(c).Within what limits did the middle of 90% of the students lie.<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 #544587 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=544587\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assuming that a plane makes a safe flight if at least half the numbers of engine run. Find whether a 6 engine plane or a 4 engine plane has a higher probability of successful flight.<BR>\n" );
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document.write( "Assuming each engine has a 50% chance of failing,<BR>\n" );
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document.write( "P(4 engine plane safe) = 1 - P(3 engines fail) = 1-(1/8) = 7/8<BR>\n" );
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document.write( "P(6 engine plane safe) = 1 - P(4 engines fail) = 1-(1/16) = 15/16<BR>\n" );
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document.write( "Ans:: 6 is safer<BR>\n" );
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document.write( "ii) The marks obtained in Probability & Statistics by 1000 students is normally distributed is normally distributed with mean 78% and standard deviation 11%. Determine (a). How many students got the marks above 90%<BR>\n" );
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document.write( "z(90) = (90-78)/11 = 12/11<BR>\n" );
document.write( "P(x > 90) = P(z > 12/11) = normalcdf(12/11,100) = 0.1377<BR>\n" );
document.write( "Ans: 0.1377*1000 = 138 students (when rounded up)<BR>\n" );
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document.write( " (b).What was the highest mark obtained by the lowest of 10% of the students <BR>\n" );
document.write( "Find the z-value with a left tail of 10%::<BR>\n" );
document.write( "invNorm(0.10) = -1.2816<BR>\n" );
document.write( "Find the corresponding \"x\" value::<BR>\n" );
document.write( "x = -1.2816*11 + 78 = 63.9<BR>\n" );
document.write( "Ans:: 63.9%<BR>\n" );
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document.write( "(c).Within what limits did the middle of 90% of the students lie.<BR>\n" );
document.write( "Find the z-value with a left tail of 5%::<BR>\n" );
document.write( "invNorm(0.05) = 1.645<BR>\n" );
document.write( "Find the corresponding x-value::<BR>\n" );
document.write( "x = -1.645*11 + 78 = 59.9<BR>\n" );
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document.write( "Lower Limit = 59.9%<BR>\n" );
document.write( "By symmetry the upper limit is 1.645*11+78 = 96.1<BR>\n" );
document.write( "Upper Limit = 96.1%<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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