### Binomial Experiment AnalysisAccording to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 24 flights are randomly selected, and the number of on-time flights is recorded.**(a) Explain why this is a binomial experiment.**The scenario described is a binomial experiment because:- **Fixed Number of Trials**: There are 24 flights, which is a fixed number.- **Two Possible Outcomes**: Each flight can either be on time or not on time.- **Independent Trials**: The on-time status of one flight does not affect another.- **Constant Probability**: Each flight has an 80% probability of being on time.**(b) Determine the values of n and p.**- **n (Number of Trials)**: 24- **p (Probability of Success)**: 0.8 (80% probability of a flight being on time)**(c) Find and interpret the probability that exactly 15 flights are on time.**To find the probability of exactly 15 flights being on time, use the binomial probability formula:\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]For 15 flights:- \( n = 24 \)- \( k = 15 \)- \( p = 0.8 \)The value can be computed to determine the probability.**(d) Find and interpret the probability that fewer than 15 flights are on time.**To find the probability that fewer than 15 flights are on time, sum the probabilities of observing 0 to 14 on-time flights.\[ P(X < 15) = \sum_{k=0}^{14} P(X = k) \]This involves calculating the sum of individual probabilities from \( P(X = 0) \) to \( P(X = 14) \). These values can be calculated using the binomial formula for each \( k \) and then summed to find the total probability.

According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 24 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 15 flights are on time. (d) Find and interpret the probability that fewer than 15 flights are on time.

According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 24 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 15 flights are on time. (d) Find and interpret the probability that fewer than 15 flights are on time.

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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According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% 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 12 flights are on time. (d) Find and interpret the probability that fewer than 12 flights are on time. (e) Find and interpret the probability that at least 12 flights are on time. (f) Find and interpret the probability that between 10 and 12 flights, inclusive, are on time.