Quantitative Techniques

28591 WordsMay 28, 2013115 Pages
DESCRIPTIVE STATISTICS & PROBABILITY THEORY 1. Consider the following data: 1, 7, 3, 3, 6, 4 the mean and median for this data are a. 4 and 3 b. 4.8 and 3 c. 4.8 and 3 1/2 d. 4 and 3 1/2 e. 4 and 3 1/3 2. A distribution of 6 scores has a median of 21. If the highest score increases 3 points, the median will become __. a. 21 b. 21.5 c. 24 d. Cannot be determined without additional information. e. none of these 3. If you are told a population has a mean of 25 and a variance of 0, what must you conclude? a. Someone has made a mistake. b. There is only one element in the population. c. There are…show more content…
All of the other passengers are sober, and will go to their proper seats unless it is already occupied; In that case, they will randomly choose a free seat. You 're person number 100. What is the probability that you end up in your seat (i.e., seat #100)?. Solution: Let’s consider seats #1 and #100. There are two possible outcomes: E1: Seat #1 is taken before #100; E2: Seat #100 is taken before #1. If any passenger takes seat #100 before #1 is taken, surely you will not end up in you own seat. But if any passenger takes #1 before #100 is taken, you will definitely end up in you own seat. By symmetry, either outcome has a probability of 0.5. So the probability that you end up in your seat is 50%. Explanation: If the drunk passenger takes #1 by chance, then it’s clear all the rest of the passengers will have the correct seats. If he takes #100, then you will not get your seat. The probabilities that he takes #1 or #100 are equal. Otherwise assume that he takes the n-th seat, where n is a number between 2 and 99. Everyone between 2 and (n-1) will get his own seat. That means the n-th passenger essentially becomes the new “drunk” guy with designated seat #1. If he chooses #1, all the rest of the passengers will have the correct seats. If he takes #100, then you will not get your seat. (The probabilities that he takes #1 or #100 are again
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