Question

According to an airline, flights on a certain route are on time 80% of the time. Suppose 10 flights are randomly selected and the number of on time flights is recorded Use technology to find the probabilities (a) Determine whether this is a binomial experiment. (b) Find and interpret the probability that exactly 8 flights are on time. (c) Find and interpret the probability that at least 8 fights are on time. (d) Find and interpret the probability that fewer than 8 flights are on time. B. No, because the probability of success differs from trial to trial C. No, because there are more than two mutually exclusive outcomes for each trial Yes, because the experiment satisfies all the criteria for a binomial experiment

Answer 1

a) D. Yes, because the experiment satisfies all the criteria for a binomial experiment
This is a binomial distribution question with
n = 10
p = 0.8
q = 1 - p = 0.2
where

P(X = x) =( b)P(X = 8), n = 10, p=0.8 X~Binomial(n = 10, p = 0.8, X = 8) /10 P(X = 8) = 0.880.210-8 (8) P(X = 8) = 45.00.880.22 = 45.00.16780.04 P(X = 8) = 0.301989888 0.302


c)P(X 8), n = 10,p = 0.8 P(X > 8) = P(8 < X < 10) P(X > 8) = P(X = 8) + P(X = 9) + P(X = 10) P(X 2 8) = (19)0.880.210-8 +(19) 0.8%0.210–9 + (19) 0.8160.210–10 P(X > 8) = 45.0(0.88)(0.22) +10.0(0.89)(0.21)+1(0.816 (0.29) P(X > 8) = 45.0(0.1678)(0.04) + 10.0(0.1342)(0.2)+1(0.1074)(1.0) P(X 8) = 0.301989888+ 0.268435456 + 0.1073741824 P(X 8) = 0.6778


d)P(X<8), n = 10,p = 0.8 P(X<8) = P(0<x<8) P(X<8)=1- P(X > 8) P(X<8) = 1-0.6778 P(X <8) = 0.3222

d)P(X<8), n = 10,p = 0.8 P(X<8) = P(0<x<8) P(X<8)=1- P(X > 8) P(X<8) = 1-0.6778 P(X <8) = 0.3222


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