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.
(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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