You are considering a bell shaped, symmetrical distribution. Using empirical rule, answer the following question: What percent of values of the distribution falls below one standard deviation of the mean? 68% 16% 2.5% 34%

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So we're working with the bell shaped symmetric distribution, so i've drawn the bell shaped symmetric distribution on the screen and you're going to use the empirical rule to answer this question. So, let's review what the empirical rule states when you're working with the bell shaped curve, the mean is in the center and if you go 1 standard deviation to the right and 1 standard deviation to the left within 1. Standard deviation of the mean will account for approximately 68 percent of the data, and because this is a bell shaped symmetric distribution. That means each piece would be equivalent to 34 percent. The empirical rule also states that, within 2 standard deviations of the mean, that means if we go 2 in each direction, so here is m and we go 2 in each direction. Then that accounts for approximately 95 percent of the data. So that means the 4 pieces. Should add up to 95 percent and since the middle 2 already add up to 68 percent, there's 27 percent still unaccounted for and when we split that 27 percent equally between the 2 remaining pieces, then each piece would be 13.5 percent. The empirical rule also states that within 3 standard deviations of the mean, so here is the mean if we go 3 standard deviations to the right or 3 standard deviations to the left. It accounts for approximately 99.7 percent and since the 6 pieces have to add up to 99.7 and the middle 4 already add up to 95. That means there's 4.7 percent to be split evenly, so we'd have 2.35 percent in the left and 2.35 percent in the right, and we know that the bell shaped curve. All parts have to add up to 1. So if we take the 100 percent for the entire curve and we subtract 99.7 percent, there is a .3 percent that is not discussed with the empirical rule and if we split those each 1 of the tails would represent a .15 percent. So this question asks what percentage of values of the distribution falls below 1 standard deviation of the mean so 1 standard deviation of the mean would be right here below would be adding these up and your answer. Choices are a 68 p percent, be 16 percent c. 2.5 percent and d 34 percent, so below 1 standard deviation from the mean, would be these added up or 16 percent. Now, if the word should have read what percent of values of the distribution falls within 1 standard deviation of the mean, then it would be 68 percent within would be referencing 1 in each direction, but this said below so we're going to go with the teen percent.

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