Question

your flight has been delayed: at denver international airport, 86% of recent flights have arrived on time. a sample of 12 flights is studied. round the probabilities to at least four decimal places. part: 0 / 4 part 1 of 4 (a) find the probability that all 12 of the flights were on time. the probability that all 12 of the flights were on time is

Explanation:

Step1: Identify the probability of a single - flight being on - time

The probability $p$ that a single flight arrives on time is $p = 0.86$.

Step2: Use the binomial probability formula for all successes

The binomial probability formula is $P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}$, where $n$ is the number of trials, $k$ is the number of successes, $C(n,k)=\frac{n!}{k!(n - k)!}$. When all 12 flights are on time, $n = 12$, $k = 12$, and $1-p=0.14$. Since $C(12,12)=\frac{12!}{12!(12 - 12)!}=1$, the probability $P(X = 12)=p^{12}$.

Step3: Calculate the probability

Substitute $p = 0.86$ into the formula: $P(X = 12)=(0.86)^{12}$.
$(0.86)^{12}\approx0.1422$

Answer:

$0.1422$