Question

According to an airline, flights on a certain route are on time 80% of the time. Suppose 20 flights are randomly selected and the number of on-time flights is recorded.
A. Find and interpret the probability that exactly 14, flights are on time
B. Find and interpret the probability that fewer than 14 flights are on time
C. Find and interpret the probability that at least 14 flights are on time.
. Find and interpret the probability that between 12 and 14 flights, inclusive, are on time.

Answer 1

Probability Mass Function is

P ( X = 14 ) = 0.1091

There is 10.91% probability that exactly 14 flight will be on time, when the probability that certain flight on time is 80%

Part b) P ( X < 14 ) = 1 - P ( X >= 14 )

P ( X < 14 ) = 1 - P ( X >= 14 ) = 1 - 0.9133 = 0.0867

P ( X < 14 ) = 0.0867

There is 8.67 % probability that less than 14 flight will be on time when the probability that certain flight on time is 80%

Part c)

P ( X >= 14 ) = 1 - P ( X < 14 ) = 1 - 0.0867 = 0.9133

There is 91.33% probability that at least 14 flight will be on time, when probability of certain flight on time is 80%

Find and interpret the probability that between 12 and 14 flights, inclusive, are on time.

P ( 12 <= X <=14 ) = P ( X = 12 ) + P ( X = 13 ) + P ( X = 14 )

P ( 12 <= X <=14 ) = 0.1858

There is 18.58% probability that between 12 and 14 flights will be on time, when certain flight on time is 80%.