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Probability

Jamieruss33

New member
Joined
Nov 4, 2009
Messages
3
I have a question regarding my stats homework and I'm not sure how to set it up. Here is the question:

An airline estimates that 97% of people booked on their flights actually show up. If the airline books 70 people on a flight for which the max number is 68, what is the probability that the number of people who show up will exceed the capacity of the plane?

Any help in explaining how to set this up would be greatly appreciated.

Thanks,

Jamie
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,708
Mean = 70 * 0.97 = 67.9
Variance = 70 * 0.97 * 0.03 = 2.037

That's a good start. Now what?
 

mathjunkie1990

New member
Joined
Nov 14, 2009
Messages
7
I understand how you got the mean and the variance but i dont know what the next step would be?
I have a similar problem.
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,708
You should first make up your mind what constitutes a "person". Really, what does 68.2 mean in this context? You can't cut people up to fit your statistical model. Let's use whole numbers obtained by 5/4 rounding. With this, we're good until 68.5 people show up.

Standard Deviation = sqrt(2.037) = 1.427

(68.5 - 67.9)/1.427 = 0.420

What is the probability from the Standard Normal that exceeds 0.420 Standard Deviations above the Mean?
 
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