28591 Words115 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

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

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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