ID Cost of Airfares in the US (domestic) 1 146 2 620 3 79 4 299 5 576 6 89 7 589 8 165 9 509 10 23 11 376 12 226 13 462 14 634 15 36 16 226 17 263 18 456 19 390 20 541 21 19 22 329 23 537 24 512 25 423 26 515 27 358 28 110 29 319 30 671 31 561 32 96 33 574 34 385 35 263 36 240 37 449 38 592 39 404 40 119 41 173 42 419 43 495 44 224 45 228 46 616 47 168 48 396 49 524 Normal Distribution Airfares (as shown in the Excel file for this week’s seminar) were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. The prices follow normal distribution. Use Excel to plot the density of the prices; You can either use pen and paper or Excel for question 2-5. Please use the z score formula to calculate the question 2-5. What is the probability that a domestic airfare is $550 or more? What is the probability that a domestic airfare is $250 or less?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
| ID | Cost of Airfares in the US (domestic) |
| 1 | 146 |
| 2 | 620 |
| 3 | 79 |
| 4 | 299 |
| 5 | 576 |
| 6 | 89 |
| 7 | 589 |
| 8 | 165 |
| 9 | 509 |
| 10 | 23 |
| 11 | 376 |
| 12 | 226 |
| 13 | 462 |
| 14 | 634 |
| 15 | 36 |
| 16 | 226 |
| 17 | 263 |
| 18 | 456 |
| 19 | 390 |
| 20 | 541 |
| 21 | 19 |
| 22 | 329 |
| 23 | 537 |
| 24 | 512 |
| 25 | 423 |
| 26 | 515 |
| 27 | 358 |
| 28 | 110 |
| 29 | 319 |
| 30 | 671 |
| 31 | 561 |
| 32 | 96 |
| 33 | 574 |
| 34 | 385 |
| 35 | 263 |
| 36 | 240 |
| 37 | 449 |
| 38 | 592 |
| 39 | 404 |
| 40 | 119 |
| 41 | 173 |
| 42 | 419 |
| 43 | 495 |
| 44 | 224 |
| 45 | 228 |
| 46 | 616 |
| 47 | 168 |
| 48 | 396 |
| 49 | 524 |
Airfares (as shown in the Excel file for this week’s seminar) were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees.
- The prices follow normal distribution. Use Excel to plot the density of the prices;
You can either use pen and paper or Excel for question 2-5. Please use the z score formula to calculate the question 2-5.
- What is the probability that a domestic airfare is $550 or more?
- What is the probability that a domestic airfare is $250 or less?
- What if the probability that a domestic airfare is between $300 and $400?
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