G. There are two mutually exclusive outcomes, success or failure. (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 0.0680 . (Round to four decimal places as needed.) Interpret the probability. 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) Using the binomial distribution, the probability that fewer than 11 flights are on time is (Round to four decimal places as needed.)
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Bonus Knowledge
Thinking about the binomial distribution can be a bit of a flighty experience! When you have \( n = 17 \) flights and the probability \( p = 0.8 \) of being on time, you can model the likelihood of various outcomes. Now, that probability of exactly 11 flights being on time, 0.0680, means that in 100 attempts at this scenario, you'd expect about 7 instances where exactly 11 flights arrive right on schedule! So, gear up — flying through probabilities can really help manage expectations! Now, for fewer than 11 flights being on time, we can calculate this by summing the probabilities of 0 to 10 flights being on time, which is totally doable with the binomial formula. But to keep it simple: you can use tables or software to find this probability. Just know that the excitement (or dread) of flights not being on time can really pile up as you run more experiments! Hold tight, your final probability will reveal just how turbulent or smooth these flight times can get!
