At a certain airport, 75% of the flights arrive on time. A sample of 10 flights is studied.

a. Find the probability that all 10 of the flights were on time.

b. Find the probability that exactly eight of the flights were on time.

c. Find the probability that eight or more of the flights were on time.

Answer :

Step 1 of 4:

Given, 75% of the flights arrive on time. A sample of 10 flights is studied

Let X follows binomial distribution with probability mass function is

P(x: n,p) = (1 - p , x = 0, 1, 2, ….., n.

Mean of the binomial distribution is

= np

Variance of the binomial distribution is

= npq

Where, n = 10 and p = 75% = 0.75

Step 2 of 4:

The claim is to find the probability that all 10 of the flights were on time.P(x = 0, 1, ….10) = P(x=0) + P(x = 1) +...............+ P(x =10)

= (1 - 0.75+ (1 - 0.75

+......+ (1 - 0.75

= 0.000000953674 + ……….. + 0.05631351

= 1

the probability that all 10 of the flights were on time is 1.