Probability

[Jamieruss33]

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]

Mean = 70 * 0.97 = 67.9
Variance = 70 * 0.97 * 0.03 = 2.037

That's a good start. Now what?

 

[mathjunkie1990]

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]

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?