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Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent t...

Question

Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.If an additional test were done on the claim of the average delay, which distributi

Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. If an additional test were done on the claim of the average delay, which distribution would you use?



Answers

Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

If an additional test were done on the claim of the average delay, which distribution would you use?

Let's take a look helps these problems. So the question is about flying time between two cities. So he says the flight time quotes to be two hour and five minutes. And you also say that according to the previous history, this move only distributed between two hour and to our 20 minutes. So if we were closest to the been born probably to distribution on page two 63 in the book, we can get the probability density function. So if we use X, who represents the flight time, the pdf should be won over. I mean, Linus, eh? And our problem A is the union, which is two hours, and he is the next month, which is two hour and 20 minutes. And if he is too late or too early, it will be zero chance will be zero. So if we bleeding the numbers for a MP, the maximum is 42 hour and minutes and minus the minimum two hour, we will get the best function or the flight time, which is one over 20. So this problem asked us for more questions. We will look at them one by one, and we always saw those We just need to remember the probability density function we just got. First question is show a graph off the probably kid density function for a pdf over uniforms distributed variable. The birth coach excess will be the probability himself. So it is of eggs and the horse. Some pill access will be variable. It's stuff. Now we paint down the mila, which is to our and the next one, which is two hour and 20 minutes. And the probability off a fly arising at any time in between this period will be equal. That is why the line is horizontal. Now we kiss connected and we got the square shape off these media or uniformly distributed variable our flight, hon X. So I get I have ah, better plots for these, uh, and we will use it or our nest next questions. So question be off. The probability off the flight being no being no more than five minutes late for these, Uh, we gonna new cats. The visual. Well, so no more than five minutes late. That is compared to our quote. Two hour and five minutes and withing five minutes. So it stays innings The flag arrived it's late as two hour and 10 minutes. If we look has the brown, the area under these orange square is the probability off the flight no more than five minutes late. And if he is on you, five person off the whole square. How would I know that? Remember the probability test a function You got ISS one over 20. So we will use the one over onesie. Multiply. Bye. The five minutes interval Because from to our five minutes, 222 hour, 10 minutes, these these off five minutes interval. So multiplied by five. And we've got won over five, which equals two, 25%. So that is how we got the probability off the life being no more than five minutes late. This 25% and next we are going to see the probability off the flight seen more than 10 minutes late. So on the graph from these heh minutes off her, the estimated to our five minutes. That was starting from to our big 10 minutes and even later. So that is tricky. So first, the graph, under between 15 minutes and 20 minutes again is won over 20 multiply bye by minutes So these five minutes is coming around the turbo between 15 minutes to quantum minutes. So that is where we get these pots. And then what happens off through that? So what happens is off her planting minutes. The probability off the flight of writing becomes zero. So that is a That is how our data is distributed. Remember the pia off our flight time? If in his anywhere else, something's if x? Yes. Waiter. Then two hours and 20 minutes, or if X is less than to our So in this case, we are all skiing. If X is greater than two hour and 20 minutes that he is zero. So the final results for the flight being more than 10 minutes late will only be this area. So that use again, I want to fly, Chris it and the final question off the expected flight time. So we will again regress to the boot. Um, huge from page 2 55 Well, look. Perhaps the function for populating the expectation value off the variable if you use a plus B divided by two. So if we loving our values for a the Minutemen, it is a two hour for be the maximum it is to our and pointing limits. And if we do, the calculation that leaves out is to our and sentiments.

Problem Number 61. We know that. Said the flight takes more than one hour on 15% of the day and just let then one over for 60 minutes on 85% of the legs. So thin person, More than one over. Uh, and 85% of course. Ah, it's a bad one. Um, but it takes more than 75 meanings on 3% of the days. And thus things that 75 minutes. So we have here. Ah, 3% more mad. 25 minutes, 1.27% Semen, crime means. And so the value or rapidly or pointed Bryant over opening Brian Setting is a prick to 1.4, um, and 1.88 So this is not the advantages, the probability. So here over really be equipped, So ah, zip vary from the papers. Christmas do this covering gates ever to 1.4 or four point baby. It was a very event on the many claimed by the pool, so we know that. Ah, the venue uh, me Plus that is a van Eugene 1.4 for 60 minutes. The mind grunts and TV's on for the 75 minutes were the same since we worked with me. How close? Ah, uh, is it ready for, uh, for 75 minutes? So if they were to appoint a date, we saw just subtract force creations. We can get that 15 equal bread. It's for semen. So a stigma is equal to a 17 point eight from 71 eso between. I need to remind me we can see that immediately. Back to 16 miners from point for breath of remembrance and the region Do you put for 41.4 to 8? It's it's

Okay, This question is your number 60. Okay, so travel time to study toe work, a study of the commuting times or towards their trouble timeto work. Of the random sample of 20 employees employed adults, 20 is gonna be the sample size, uh, adult in New York steak. So the average the mean is expire as given as 31.25 minutes, and standard deviation is 21.8 minutes. So what is the standard error of to me the scanner era of the me? Okay. Dinner error of the mean is computed by a during the standard deviation divided by the square root of the sample size end. So we do 21 1 88 minutes on divide by the end squirt of 20 to do the calculation. This is approximately 4.89 to 5 minutes. So this dinner error of the mean we're presents the average distance run. The symbol means to the population me uncle mean to the population. Trust me, IHS, Approximately 4.89 to 5 minutes after that is still ah, meaning of this dinner era of the meat

40. Which distribution should you use for this problem? Well, in this particular situation were given 70 patients and a sample mean and sample Senate aviation because we're not given the population center deviation, just the sample standard deviation, the best distribution to use. In this case, it's the tea distribution.


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