According to an airline, flights on a certain route are on time 80% of the time.

Question

According to an airline, flights on a certain route are on time 80% of the time. Suppose 20 flights are randomly selected and the number of on time flights is recorded. Use technology to find the probabilities. Use the Tech Help button for further assistance. Determine whether this is a binomial experiment. Find and interpret the probability that exactly 18 flights are on time. Find and interpret the probability that at least 18 flights are on time. Find and interpret the probability that fewer than 18 flights are on time. Find and interpret the probability that between 17 and 19 flights, inclusive, are on time. Does the probability experiment represent a binomial experiment? No, because the probability of success differs from trial to trial. Yes, because the experiment satisfies all the criteria for a binomial experiment. No, because there are more than two mutually exclusive outcomes for each trial. No, because the trials of the experiment are not independent. The probability that at least 18 flights are on time is. (Round to four decimal places as needed.) Choose the correct answer below. In 100 trials of this experiment, we expect about 21 to result in at least 18 flights being on time. In 100 trials of this experiment, we expect about 79 to result in at least 18 flights being on time. In 100 trials of this experiment, we expect about 18 to result in at least 14 flights being on time. In 100 trials of this experiment, we expect about 14 to result in at least 18 flights being on time.

Explanation / Answer

Font size is extremely low to interpret the numbers.

a) This is a binomial distribution, with probability of success, p=0.87, number of trials, n=20 and number of success in n trials denoted by r. P(X,r)=nCr(p)^r(q)^n-r

b) P(X=18)=20C18(0.87)^18(0.13)^2=0.2618

c) P(X>=18)=1-P(X<18)=1-0.4920=0.5080

d) P(X<18)=0.4920

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