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?

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So you are considering a bell shaped symmetric distribution, so i have drawn that bell shaped symmetric distribution and we're going to use the empirical rule and the empirical rule states that your mean would be in the center of this bell shaped curve and within 1 standard deviation Of the mean meaning, if you go 1 standard deviation to the right or 1 standard deviation to the left, it will account for approximately 68 percent of the data. So that means you would have 34 percent in each piece because of the symmetric nature of the bell. They would be the same size. The empirical rule also states that, within 2 standard deviations of the mean there is approximately 95 percent of the data. So that means the 4 pieces have to add up to 95 percent and the middle to already add up to 68 percent. So that means there's 27 percent to be split evenly between the next 2 pieces. So we'd have 13.5 percent here and 13.5 percent over here, and the empirical rule also states that within 3 standard deviations of the mean you will find approximately 99.7 percent. So that means the 6 pieces in between these 2 white arrows should total up to 99.7, and since the 4 middle pieces already add up to 99 are sorry 95 percent. That means there there's 4.7 percent to be split evenly. So each piece here would be 2.35 percent and then finally keep in mind that the entire bell does add up to 100 percent in. So if you take 100 percent minus the 99.7 percent, there's .3 percent- that is split between the 2, so that would make each 1 to be .15 percent. That'S left over in these final tails, so your question says what percentage of values of the distribution falls below 1 standard deviation of the mean so below 1 standard deviation of the mean. So if we say we went 1 standard deviation and we're talking about below. If we were to add up these pieces here, it would total up to 16 percent. Now, if it said within 1, within 1 standard deviation, instead of below 1 standard deviation. If it was within 1 standard deviation of the men, we would be talking about 68 perc.

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