document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983113>Question 983113</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A one-plane airline has a passenger capacity of 120.  The number of passengers on a flight is normally distributed with a mean of 90 and a standard deviation of 15. <BR>\n" );
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document.write( "1. What is the probability that a flight will be “overbooked” (ie not able to get a seat on the flight)?  \r<BR>\n" );
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document.write( "2. If there are 5 flights a day, every day, how many flights will be overbooked in a 30 day month?\r<BR>\n" );
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document.write( "Please help! and explain! Thanks so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #603929 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=603929\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "X = number of tickets sold\r<BR>\n" );
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document.write( "\"Overbooked\" means that more than 120 tickets have been sold. <BR>\n" );
document.write( "So when X > 120, the flight has been overbooked.<BR>\n" );
document.write( "We want to find the probability P(X > 120)\r<BR>\n" );
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document.write( "Let x = 120. Find the z-score<BR>\n" );
document.write( "z = (x-mu)/sigma<BR>\n" );
document.write( "z = (120-90)/15<BR>\n" );
document.write( "z = 30/15<BR>\n" );
document.write( "z = 2\r<BR>\n" );
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document.write( "Use this z-score to find the value of P(Z < 2). I'm going to use a table, but you can use a TI calculator. The normalcdf function gets the job done.\r<BR>\n" );
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document.write( "I used a <a  rel=nofollow HREF=\"https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf\">table</a> to find that P(Z < 2) = 0.97725\r<BR>\n" );
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document.write( "So,\r<BR>\n" );
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document.write( "P(Z > 2) = 1 - P(Z < 2)<BR>\n" );
document.write( "P(Z > 2) = 1 - 0.97725<BR>\n" );
document.write( "P(Z > 2) = 0.02275\r<BR>\n" );
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document.write( "Therefore, \r<BR>\n" );
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document.write( "P(X > 120) = P(Z > 2)<BR>\n" );
document.write( "P(X > 120) = 0.02275\r<BR>\n" );
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document.write( "The probability of overbooking is 0.02275<BR>\n" );
document.write( "There's a 2.275% chance that the flight is overbooked.\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "Multiply the probability with the number of flights per day.\r<BR>\n" );
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document.write( "0.02275*5 = 0.11375\r<BR>\n" );
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document.write( "So on average, we expect 0.11375 flights per day to be overbooked. On any given day, this is a good thing since the number is small. If we extend this over 30 days, then 30*0.11375 = 3.4125\r<BR>\n" );
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document.write( "So over 30 days, we expect on average roughly 3.4125 flights to be overbooked. </SPAN>\n" );
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