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According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 17 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) Identify the statements that explain why this is a binomial experiment. Select all that apply. A. The probability of success is the same for each trial of the experiment. B. The experiment is performed a fixed number of times. C. There are three mutually exclusive possible outcomes, arriving on-time, arriving early, and arriving late. D. There are two mutually exclusive outcomes, success or failure. E. Each trial depends on the previous trial. F. The experiment is performed until a desired number of successes are reached. G. The trials are independent. H. The probability of success is different for each trial of the experiment. (b) Using the binomial distribution, determine the values of n and p. n = 17 (Type an integer or a decimal. Do not round.) p = 0.80 (Type an integer or a decimal. Do not round.) (c) Using the binomial distribution, the probability that exactly 11 flights are on time is (Round to four decimal places as needed.)

According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 17 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) Identify the statements that explain why this is a binomial experiment. Select all that apply. A. The probability of success is the same for each trial of the experiment. B. The experiment is performed a fixed number of times. C. There are three mutually exclusive possible outcomes, arriving on-time, arriving early, and arriving late. D. There are two mutually exclusive outcomes, success or failure. E. Each trial depends on the previous trial. F. The experiment is performed until a desired number of successes are reached. G. The trials are independent. H. The probability of success is different for each trial of the experiment. (b) Using the binomial distribution, determine the values of n and p. n = 17 (Type an integer or a decimal. Do not round.) p = 0.80 (Type an integer or a decimal. Do not round.) (c) Using the binomial distribution, the probability that exactly 11 flights are on time is (Round to four decimal places as needed.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The task involves analyzing American Airlines flights from Dallas to Chicago, which are on time 80% of the time. A sample of 17 flights is examined to determine the number of on-time flights. The questions are as follows: (a) **Explain why this is a binomial experiment.** To classify this as a binomial experiment, the following criteria are validated: - The probability of success remains constant across all trials: Each flight has the same probability (80%) of being on time. - There are two mutually exclusive outcomes: A flight is either on time (success) or not (failure). - The trials are independent: Each flight’s punctuality is independent of others. - The number of trials is fixed: There are a total of 17 trials (flights). (b) **Using the binomial distribution, determine the values of n and p.** - \( n = 17 \) (number of trials) - \( p = 0.80 \) (probability of success) (c) **Using the binomial distribution, find the probability that exactly 11 flights are on time.** This requires using the binomial probability formula for finding the likelihood of 11 successes (on-time flights) out of 17, given a success probability of 0.80. Further parts of the exercise will involve calculating probabilities using the binomial distribution for fewer than 11 flights, at least 11 flights, and between 9 and 11 flights being on time. These calculations typically involve binomial probability functions or statistical software for precision.
Transcribed Image Text:The task involves analyzing American Airlines flights from Dallas to Chicago, which are on time 80% of the time. A sample of 17 flights is examined to determine the number of on-time flights. The questions are as follows: (a) **Explain why this is a binomial experiment.** To classify this as a binomial experiment, the following criteria are validated: - The probability of success remains constant across all trials: Each flight has the same probability (80%) of being on time. - There are two mutually exclusive outcomes: A flight is either on time (success) or not (failure). - The trials are independent: Each flight’s punctuality is independent of others. - The number of trials is fixed: There are a total of 17 trials (flights). (b) **Using the binomial distribution, determine the values of n and p.** - \( n = 17 \) (number of trials) - \( p = 0.80 \) (probability of success) (c) **Using the binomial distribution, find the probability that exactly 11 flights are on time.** This requires using the binomial probability formula for finding the likelihood of 11 successes (on-time flights) out of 17, given a success probability of 0.80. Further parts of the exercise will involve calculating probabilities using the binomial distribution for fewer than 11 flights, at least 11 flights, and between 9 and 11 flights being on time. These calculations typically involve binomial probability functions or statistical software for precision.
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According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 17 flights are randomly selected, and the number of on-time flights is recorded. ### (a) Explain why this is a binomial experiment. Identify the statements that explain why this is a binomial experiment. Select all that apply. - ✅ A. The probability of success is the same for each trial of the experiment. - ✅ B. The experiment is performed a fixed number of times. - ⬜ C. There are three mutually exclusive possible outcomes, arriving on-time, arriving early, and arriving late. - ✅ D. There are two mutually exclusive outcomes, success or failure. - ⬜ E. Each trial depends on the previous trial. - ⬜ F. The experiment is performed until a desired number of successes are reached. - ✅ G. The trials are independent. - ⬜ H. The probability of success is different for each trial of the experiment. ### (b) Determine the values of n and p. - \( n = 17 \) (Type an integer or a decimal. Do not round.) - \( p = 0.80 \) (Type an integer or a decimal. Do not round.) ### (c) Find and interpret the probability that exactly 11 flights are on time. Using the binomial distribution, the probability that exactly 11 flights are on time is \( 0.0680 \). (Round to four decimal places as needed.) **Interpretation:** In 100 trials of this experiment, it is expected that about 7 will result in exactly 11 flights being on time. (Round to the nearest whole number as needed.) ### (d) Find and interpret the probability that fewer than 11 flights are on time. Using the binomial distribution, the probability that fewer than 11 flights are on time is \( 0.0377 \). (Round to four decimal places as needed.) **Interpretation:** In 100 trials of this experiment, it is expected that about 4 will result in fewer than 11 flights being on time. (Round to the nearest whole number as needed.) ### (e) Find and interpret the probability that at least 11 flights are on time. Using the binomial distribution, the probability that at least 11 flights are on time is \( 0.9623 \). (Round to four decimal places as
Transcribed Image Text:According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 17 flights are randomly selected, and the number of on-time flights is recorded. ### (a) Explain why this is a binomial experiment. Identify the statements that explain why this is a binomial experiment. Select all that apply. - ✅ A. The probability of success is the same for each trial of the experiment. - ✅ B. The experiment is performed a fixed number of times. - ⬜ C. There are three mutually exclusive possible outcomes, arriving on-time, arriving early, and arriving late. - ✅ D. There are two mutually exclusive outcomes, success or failure. - ⬜ E. Each trial depends on the previous trial. - ⬜ F. The experiment is performed until a desired number of successes are reached. - ✅ G. The trials are independent. - ⬜ H. The probability of success is different for each trial of the experiment. ### (b) Determine the values of n and p. - \( n = 17 \) (Type an integer or a decimal. Do not round.) - \( p = 0.80 \) (Type an integer or a decimal. Do not round.) ### (c) Find and interpret the probability that exactly 11 flights are on time. Using the binomial distribution, the probability that exactly 11 flights are on time is \( 0.0680 \). (Round to four decimal places as needed.) **Interpretation:** In 100 trials of this experiment, it is expected that about 7 will result in exactly 11 flights being on time. (Round to the nearest whole number as needed.) ### (d) Find and interpret the probability that fewer than 11 flights are on time. Using the binomial distribution, the probability that fewer than 11 flights are on time is \( 0.0377 \). (Round to four decimal places as needed.) **Interpretation:** In 100 trials of this experiment, it is expected that about 4 will result in fewer than 11 flights being on time. (Round to the nearest whole number as needed.) ### (e) Find and interpret the probability that at least 11 flights are on time. Using the binomial distribution, the probability that at least 11 flights are on time is \( 0.9623 \). (Round to four decimal places as
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