Question

American Airlines' flights from Chicago to Atlanta are on time 70 % of the time. Suppose 9 flights are randomly selected, and the number on-time flights is recorded.
Round answers to 3 significant figures.

The probability that exactly 7 flights are on time is =

The probability that at most 3 flights are on time is =

The probability that at least 4 flights are on time is =

Answer 1

American Airlines' flights from Chicago to Atlanta are on time 70 % of the time. i.e P = 0.7

n = 9

Let , X be number of  on-time flights .

X follows Binomial distribution with n = 9 and p = 0.7

a)

We have to find probability that exactly 7 flights are on time.

i.e we have to find P( x = 7 )

Using Excel function , =BINOMDIST( x , n , p , 0 )

P( x = 7 ) = BINOMDIST(7,9,0.7,0 ) = 0.267

The probability that exactly 7 flights are on time is 0.267

b )

We have to find probability that at most 3 flights are on time .

i.e we have to find P( x <= 3 )

Using Excel function , =BINOMDIST( x , n , p , 1 )

P( x <= 3 ) = BINOMDIST(3,9,0.7,1 ) = 0.025

The probability that at most 3 flights are on time is 0.025

c)

We have to find probability that at least 4 flights are on time

i.e we have to find P( x >= 4 )

P( x >= 4 ) = 1 - P( x <= 3 )

From part b, P( x <= 3 ) = 0.025

So, P( x >= 4 ) = 1 - 0.025 = 0.975

The probability that at least 4 flights are on time is 0.975