Question

The number of flights taking off from Barcelona el Prat airport between 1:00?.?. and 12:00p.?. was observed and recorded on every weekday morning of year 2019. The statistics revealed that the number of flights are distributed according to a Gaussian distribution with mean 720 and standard deviation 40. Answer the following items and justify your answer with a plot illustrating the statistical information.

1. What is the probability that on a weekday, between 1am an12pm, the number of flights is between 640 and 800?.
2. What is the probability that, in the same time slot, the number of flights be at most 640? And more than 800?

Answer 1

a)

Given :- = 720 , = 40 )
We convet this to Standard Normal as
P(X < x) = P( Z < ( X - ) / )
P ( 640 < X < 800 ) = P ( Z < ( 800 - 720 ) / 40 ) - P ( Z < ( 640 - 720 ) / 40 )
= P ( Z < 2) - P ( Z < -2 )
= 0.9772 - 0.0228
= 0.9545

b)

P( X < 640 ) = P ( Z < 640 - 720 ) / 40 )
= P ( Z < -2 )
P ( X < 640 ) = 0.0228

c)

P ( X > 800 ) = P(Z > (800 - 720 ) / 40 )
= P ( Z > 2 )
= 1 - P ( Z < 2 )
= 1 - 0.9772

= 0.0228