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On Assignment 11.15, you found the mean and standard deviation for X, the number of dots facing up when a single die is rolled. You may want to pause and look over the solutions to MAC15. These are copied, for your convenience, on the back of this page. We found that the mean is u = 3.5 and the standard deviation is o = 1.7078. Now, suppose that instead of tossing one die and counting the number of dots facing up we toss two dice and let X =the mean number of dots facing up on the two dice. Note that when tossing 2 dice, x could end up being 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, or 6.0. X is a random variable. We call the expected value (also known as the mean) of this random variable E( X ) or H. Your text uses the symbol A. The standard deviation of , also called the standard error of the mean is denoted by the symbol O. It is easy to calculate once you know o, which you found on MAC15. Review Chapter 7 if you've orgotten the formula. Then complete the following sentence: When tossing two dice and finding the mean, Xwe find that has a mean or expected value, ミク and a standard deviation Finally, suppose that instead of tossing two dice and finding the mean we were to toss five dice and record the mean for those five dice. Consider how this might (or might not) change the expected value and the standard deviation of the sample mean. Repeat this for larger samples of 10, 20, and 50 dice. Complete the table below using decimals rounded to four decimal places where necessary. Mean or expected Standard deviation of Number of dice tossed value of x. Note that x. Note that for n=1, from which we'll find for n=1, this is the this is the standard the sample mean, I mean for the roll of a deviation for the roll of single die. a single die. n or 1 3.5 1.7078 5 10 20 50

On Assignment 11.15, you found the mean and standard deviation for X, the number of dots facing up when a single die is rolled. You may want to pause and look over the solutions to MAC15. These are copied, for your convenience, on the back of this page. We found that the mean is u = 3.5 and the standard deviation is o = 1.7078. Now, suppose that instead of tossing one die and counting the number of dots facing up we toss two dice and let X =the mean number of dots facing up on the two dice. Note that when tossing 2 dice, x could end up being 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, or 6.0. X is a random variable. We call the expected value (also known as the mean) of this random variable E( X ) or H. Your text uses the symbol A. The standard deviation of , also called the standard error of the mean is denoted by the symbol O. It is easy to calculate once you know o, which you found on MAC15. Review Chapter 7 if you've orgotten the formula. Then complete the following sentence: When tossing two dice and finding the mean, Xwe find that has a mean or expected value, ミク and a standard deviation Finally, suppose that instead of tossing two dice and finding the mean we were to toss five dice and record the mean for those five dice. Consider how this might (or might not) change the expected value and the standard deviation of the sample mean. Repeat this for larger samples of 10, 20, and 50 dice. Complete the table below using decimals rounded to four decimal places where necessary. Mean or expected Standard deviation of Number of dice tossed value of x. Note that x. Note that for n=1, from which we'll find for n=1, this is the this is the standard the sample mean, I mean for the roll of a deviation for the roll of single die. a single die. n or 1 3.5 1.7078 5 10 20 50

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Statistics: Assignment 17.30** **Dice Roll Analysis** **Background:** In Assignment 11.15, we evaluated the mean and standard deviation for \( X \), which represents the number of dots facing up when a single die is rolled. Here, the mean calculated was \( \mu = 3.5 \) and the standard deviation was \( \sigma = 1.7078 \). **Scenario:** Now, consider tossing two dice and calculating the mean number of dots facing up. Let \( \overline{X} \) be the mean number of dots facing up on the two dice. For two dice, \( \overline{X} \) could range from 1.0 to 6.0 in increments of 0.5 (e.g., 1.0, 1.5, ..., 6.0). **Random Variables:** The expected value, or mean, of this random variable \( \overline{X} \) is denoted by \( E(\overline{X}) \) or \( \mu_{\overline{X}} \). **Standard Deviation:** The standard deviation of \( \overline{X} \), also known as the standard error of the mean, is denoted by \( \sigma_{\overline{X}} \). This is calculated easily if you know \( \sigma \). **Exercises:** Complete the sentence: - When tossing two dice and finding the mean, \( \overline{X} \), the mean or expected value \( \mu_{\overline{X}} = \) ________ and a standard deviation \( \sigma_{\overline{X}} = \) ________. Next, consider tossing five dice and finding the mean, and how it affects the expected value and standard deviation. Repeat this for samples of 10, 20, and 50 dice. **Table Completion:** | Number of dice tossed from which we’ll find the sample mean, \( \overline{X} \) \( (n) \) | Mean or expected value of \( \overline{X} \) \( E(\overline{X}) \) or \( \mu_{\overline{X}} \) | Standard deviation of \( \overline{X} \) \( \sigma_{\overline{X}} \) | |---|---|---| | 1 | 3.5
Transcribed Image Text:**Statistics: Assignment 17.30** **Dice Roll Analysis** **Background:** In Assignment 11.15, we evaluated the mean and standard deviation for \( X \), which represents the number of dots facing up when a single die is rolled. Here, the mean calculated was \( \mu = 3.5 \) and the standard deviation was \( \sigma = 1.7078 \). **Scenario:** Now, consider tossing two dice and calculating the mean number of dots facing up. Let \( \overline{X} \) be the mean number of dots facing up on the two dice. For two dice, \( \overline{X} \) could range from 1.0 to 6.0 in increments of 0.5 (e.g., 1.0, 1.5, ..., 6.0). **Random Variables:** The expected value, or mean, of this random variable \( \overline{X} \) is denoted by \( E(\overline{X}) \) or \( \mu_{\overline{X}} \). **Standard Deviation:** The standard deviation of \( \overline{X} \), also known as the standard error of the mean, is denoted by \( \sigma_{\overline{X}} \). This is calculated easily if you know \( \sigma \). **Exercises:** Complete the sentence: - When tossing two dice and finding the mean, \( \overline{X} \), the mean or expected value \( \mu_{\overline{X}} = \) ________ and a standard deviation \( \sigma_{\overline{X}} = \) ________. Next, consider tossing five dice and finding the mean, and how it affects the expected value and standard deviation. Repeat this for samples of 10, 20, and 50 dice. **Table Completion:** | Number of dice tossed from which we’ll find the sample mean, \( \overline{X} \) \( (n) \) | Mean or expected value of \( \overline{X} \) \( E(\overline{X}) \) or \( \mu_{\overline{X}} \) | Standard deviation of \( \overline{X} \) \( \sigma_{\overline{X}} \) | |---|---|---| | 1 | 3.5
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