S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
It is currently Thu, 24 Jul 2014 11:39:50 UTC

All times are UTC [ DST ]




Post new topic Reply to topic  [ 2 posts ] 
Author Message
PostPosted: Sun, 22 Apr 2012 00:16:14 UTC 
Offline
Member

Joined: Wed, 15 Feb 2012 07:19:33 UTC
Posts: 31
An airline sells 108 tickets for her daily flight from Tokyo to Los Angeles. On average, 4% of customers who have purchased tickets do not turn up. Let X represent the number of customers who do not turn up for this flight.

ii) Find the probability that the mean number of empty seats for each daily flight is at most 4, in a randomly chosen 60-day period.
iii) By using a suitable approximation, find the least number of consecutive days in which the probability of at least 6 customers do not turn up exceeds 0.999.

the answer for ii) is 0.112 and the answer for iii) is 4. But I've spent a very long time working through the question and none of my methods seem correct. If you can explain, please do! Thanks.


Top
 Profile  
 
PostPosted: Sun, 22 Apr 2012 05:43:00 UTC 
Offline
Moderator
User avatar

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6777
Location: On this day Taiwan becomes another Tiananmen under Dictator Ma.
thesocialnetwork wrote:
An airline sells 108 tickets for her daily flight from Tokyo to Los Angeles. On average, 4% of customers who have purchased tickets do not turn up. Let X represent the number of customers who do not turn up for this flight.

ii) Find the probability that the mean number of empty seats for each daily flight is at most 4, in a randomly chosen 60-day period.
iii) By using a suitable approximation, find the least number of consecutive days in which the probability of at least 6 customers do not turn up exceeds 0.999.

the answer for ii) is 0.112 and the answer for iii) is 4. But I've spent a very long time working through the question and none of my methods seem correct. If you can explain, please do! Thanks.


Looks like someone forgot continuity correction. Binomial(108*60,0.04)~N(259.2,248.832), probability at most 240.5 is \Phi(\frac{240.5-259.2}{\sqrt{248.832}})=0.1179. If you use 240 instead, then you get 0.1117.

Similar for (iii), you want the critical n such that \dfrac{6.5-4.32n}{\sqrt{4.1712n}}=-3.0902, i.e. n=4.64.

_________________
\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 2 posts ] 

All times are UTC [ DST ]


Who is online

Users browsing this forum: No registered users


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Search for:
Jump to:  
cron
Contact Us | S.O.S. Mathematics Homepage
Privacy Statement | Search the "old" CyberBoard

users online during the last hour
Powered by phpBB © 2001, 2005-2011 phpBB Group.
Copyright © 1999-2013 MathMedics, LLC. All rights reserved.
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA