# 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 ]

 Page 1 of 1 [ 2 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: binomial distribution + approximationPosted: Sun, 22 Apr 2012 00:16:14 UTC
 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

 Post subject: Re: binomial distribution + approximationPosted: Sun, 22 Apr 2012 05:43:00 UTC
 Moderator

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 . If you use 240 instead, then you get 0.1117.

Similar for (iii), you want the critical n such that , i.e. n=4.64.

_________________

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 2 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

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

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous