![]() ![]() The mean for the standard normal distribution is zero, and the standard deviation is one. A Statistical rule States that for a normal distribution, almost all data will fall within three standard deviation of the mean. For example, if the mean of a normal distribution is five and the standard deviation is two, the value 11 is three standard deviations above (or to the right of) the mean. Step 2: Using the Empirical Rule, find the percentage (s) that corresponds with the range of values. Assuming the distribution of time is approximately normal, about what percentage of times are between 25. Answer and Explanation: 1 The Empirical Rule tells us that 68 of observations fall within a single standard deviation of the. A z-score is measured in units of the standard deviation. Step 1: Determine how far the range of values is from the mean. What values are 2 standard deviations from the mean b. The Empirical Rule is also known as the 68-95-99.7 Rule. So there is a 34 + 14 48 chance that a student will score between 81 and 74. Using the Empirical Rule, we can see that about 34 + 14 of scores are BETWEEN the mean and the second deviation below it. ![]() So, a score of 74 is 81 3.5 3.5 74 or TWO deviations below the mean. Chebyshev’s Theorem compared to The Empirical Rule The Empirical Rule also describes the proportion of data that fall within a specified number of standard deviations from the mean. Because the empirical rule gives you the percentages of the total data (if normally distributed) that are between or above or below values that are one. Because each deviation in this question is 3.5 points. The standard normal distribution is a normal distribution of standardized values called z-scores. Using the table above, you know that at least 75 of the scores will fall within the range of 65 85. The empirical rule can be broken down into three parts: (1): 68 of data falls within the first standard deviation from the mean (2): 95 fall within two standard deviations (3): 99.7 fall within three standard deviations. ![]() Recognize the standard normal probability distribution and apply it appropriately. ![]()
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