Your flight has been delayed: At Denver International...

Your flight has been delayed: At Denver International Airport, 85% of recent flights have arrived on time. A sample of 14 flights is studied. Round the probabilities to four decimal places. (a) Find the probability that all 14 of the flights were on time. The probability that all 14 of the flights were on time is. (b) Find the probability that exactly 12 of the flights were on time. The probability that exactly 12 of the flights were on time is. (c) Find the probability that 12 or more of the flights were on time. The probability that 12 or more of the flights were on time is. (d) Would it be unusual for 13 or more of the flights to be on time? It (Choose one) be unusual for 13 or more of the flights to be on time since the probability is.

Transcript

00:01 We are looking at the proportion of flights that arrive on time at denver international airport.

00:05 We have a sample of 14 flights and we expect 85 % of them to be on time.

00:12 So probability of each being on time, 0 .85.

00:16 What is the probability for part a that they are all on time? so the key here is that we have to assume these are independent trials.

00:24 So that each flight is not affecting the others.

00:28 And because of that, we can combine the probabilities by multiplicating.

00:31 So for each flight, probability being on time is 0 .85, multiply it by itself 14 times, to get the probability that all of them are on time.

00:43 So that is 0 .10 to 8 to 4 decimal places.

00:50 Part b, the probability that's exactly 12 are on time.

00:54 So this becomes a bit more complicated.

00:57 And i'm going to use the binomial formula here, because this is a binomial distribution.

01:02 Independent trials, two outcomes per trial, one time or not, same probability for each.

01:08 0 .85 being on time for each plane.

01:13 Probability that exactly x are on time is n choose x, p to the x, 1 minus p to the n minus x.

01:21 So for 12, this term is for the 12 better on time.

01:27 0 .85, multiplied by itself 12 times.

01:30 This is for the 2 better not.

01:34 They're part of a 15 % multiplied by itself.

01:38 But this is now the probability that the first 12 planes are on time and the next two are delayed.

01:45 That's 12 out of 14, but it's not the only order that might happen in.

01:49 There are many different orders of on time and delayed that you could put these planes in.

01:54 And we have to account for all of them, because they're all 12 out of 14.

01:58 This term tells you how many orders there are.

02:01 So it's 14 choose 12, your calculator should have a button like this.

02:05 14 choose 12 is 91.

02:11 Now this product is the probability of exactly 12 being one time, which is 0 .29 -1 -2...

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