Question

# According to an​ airline, flights on a certain route are on time 75% of the time....

According to an​ airline, flights on a certain route are on time 75% of the time. Suppose 20 flights are randomly selected and the number of​ on-time flights is recorded.

​(a) Explain why this is a binomial experiment.

​(b) Determine the values of n and p.

​(c) Find and interpret the probability that exactly 11 flights are on time.

​(d) Find and interpret the probability that fewer than 11 flights are on time.

​(e) Find and interpret the probability that at least 11 flights are on time.

​(f) Find and interpret the probability that between 9 and 11 flights, inclusive, are on time.

#### Homework Answers

Answer #1

​(a) Explain why this is a binomial experiment.

probability of success is fixed = 0.75

and is independent of trials

​(b) Determine the values of n and p.

n = 20 , p = 0.75

​(c) Find and interpret the probability that exactly 11 flights are on time.

P(X = k) = nCk p^k * (1- p)^(n-k)

P(X = 11) = 0.02706075

dbinom(11,20,0.75)
[1] 0.02706075

​(d) Find and interpret the probability that fewer than 11 flights are on time.

P(X < 11) = P(X<= 10) = 0.01386442

pbinom(10,20,0.75)
[1] 0.01386442

​(e) Find and interpret the probability that at least 11 flights are on time.

P(X >= 11) =1-P(X <=10)=1-0.01386442=0.9861356

​(f) Find and interpret the probability that between 9 and 11 flights, inclusive, are on time.

P(9<= X<= 11)

=0.03998978

pbinom(11,20,0.75)-pbinom(8,20,0.75)
[1] 0.03998978

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