document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=270362>Question 270362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of time a domestic flight must wait between gate departure and takeoff taxi at BWI International Airport is approximately normally distributed with a mean of 22 minutes and a standard deviation of 7 minutes.<BR>\n" );
document.write( "a. what is the probability that a plane must wait between 18 and 24 minutes before taxiing for takeoff after leaving the gate?<BR>\n" );
document.write( "b. what is the probability a plane must wait between 22 and 30 minutes before taxiing for takeoff after leaving the gate?<BR>\n" );
document.write( "c. what is the probability a plane waits more than 12 minutes between gate departure takeoff taxi?<BR>\n" );
document.write( "d. what is the length of time such that only 5% of planes wait this long or longer before gate departure and taxiing down the runway?\r<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 #198115 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=198115\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The length of time a domestic flight must wait between gate departure and takeoff taxi at BWI International Airport is approximately normally distributed with a mean of 22 minutes and a standard deviation of 7 minutes.<BR>\n" );
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document.write( "a. what is the probability that a plane must wait between 18 and 24 minutes before taxiing for takeoff after leaving the gate?<BR>\n" );
document.write( "z(18) = (18-22)/7 = -4/7<BR>\n" );
document.write( "z(24) = (24-22)/7 =  2/7<BR>\n" );
document.write( "P(18< x <24) = P(-4/7 < z < 2/7) = 0.3286<BR>\n" );
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document.write( "b. what is the probability a plane must wait between 22 and 30 minutes before taxiing for takeoff after leaving the gate?<BR>\n" );
document.write( "Ans: Same procedure as above.\r<BR>\n" );
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document.write( "c. what is the probability a plane waits more than 12 minutes between gate departure takeoff taxi?<BR>\n" );
document.write( "z(12) = (12-22)/7 = -10/7 = -1.4286<BR>\n" );
document.write( "P(x > 12) = P(z > -1.4286)<BR>\n" );
document.write( "Note: z = -1.4286 is a point 1.4286 standard deviations to the<BR>\n" );
document.write( "left of the mean.  You want the area under the normal curve that<BR>\n" );
document.write( "is to the right of -1.4286.  Use Your z-chart or calculator, if<BR>\n" );
document.write( "you have one. <BR>\n" );
document.write( "Using a TI calculator I get normalcdf(-1.4286,100) = 0.9234<BR>\n" );
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document.write( "Comment: If these calculations are a mystery I would strongly <BR>\n" );
document.write( "suggest you use a sketch of the normal curve as you work each<BR>\n" );
document.write( "problem.  That is so you can see where your x-values, z-values,<BR>\n" );
document.write( "and areas under the curve really are.  You will better understand<BR>\n" );
document.write( "what is going on when you get the answers.\r<BR>\n" );
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document.write( "d. what is the length of time such that only 5% of planes wait this long or longer before gate departure and taxiing down the runway?<BR>\n" );
document.write( "Ans: Find the z-value that corresponds to a left-tail of 5%.<BR>\n" );
document.write( "invNorm(0.5) = -1.645<BR>\n" );
document.write( "Find the corresponding x-value:<BR>\n" );
document.write( "x = zs + u<BR>\n" );
document.write( "x = -1.645*7 + 22<BR>\n" );
document.write( "x = 10.485 minutes<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
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