C. Each trial depends on the previous trial. D. The experiment is performed a fixed number of times. E. The probability of success is different for each trial of the experiment. G. The trials are independent. H. The probability of success is the same 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.) \( p=0.8 \) (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.)
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Bonus Knowledge
When dealing with the binomial distribution, you're exploring scenarios where there are fixed numbers of trials, and each trial has two possible outcomes, like success (a flight is on time) or failure (a flight is late). Fun fact: the binomial distribution is a key concept in statistics, widely used in everything from quality control in manufacturing to predicting outcomes in sports events! To find the probability of exactly 11 successful flights out of 17, you would use the binomial probability formula: \[ P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k} \] where \( n \) is the number of trials, \( k \) is the number of successes, \( p \) is the probability of success, and \( (1 - p) \) is the probability of failure. Plugging in your values: \[ P(X = 11) = \binom{17}{11} (0.8)^{11} (0.2)^{6} \] Calculating this will give you the exact probability for 11 flights being on time; don’t forget to round your answer to four decimal places! You got this!
