Question

According to an airline, flights on a certain route are on time 80% of the time. Suppose 8 flights are randomly selected and the number of on time flights is recorded. Use technology to find the probabilities.

(a) Determine whether this a binomial experiment.

(b) Find and interpret the probability that exactly 6 flights are on time.

(c) Find and interpret the probability that fewer than 6 flights are on time.

(d) Find and interpret the probability that at least 6 flights are on time

(e) Find and interpret the probability that between 5 and 7 flights, inclusive, are on time.

Answer 1

a)

conditions for binomial experiment.

*the experiment should consists of fixed number of trails(FLIGHTS),that is n=8

*Each trail has two outcomes (on time or not on time)

*probability of success is constant(p=0.8)

*trials are identical and independent.

given problem is satisfies all the conditions of binomial experiment so it is a binomial experiment.

b)

There is 29.36% chance that exactly 6 flights on time.

c)

using formula we get

There is 20.3% chance that less than 6 flights are on time.

d)

There is 79.69% chance that at least 6 flights are on time.

e)

There is 77.59%% chance that between 5 and 7(inclusive) flights are on time.