1. Using Normal Distributions
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Use the given diagram of normal distribution and treat each grid as 1% of the area below the normal curve.
See solution.
We are asked to determine approximately what percent of data lies within one, two, and three standard deviations of the mean. To do so, let's take a look at the given diagram that presents a normal distribution.
We are given that each square on the grid represents 1%. This means we can count the number of squares that are within each interval and this number will represent the percent of the data we are looking for. Notice that we will need to approximate the result because in some cases the whole square is not shaded.
Now we are ready to find the appropriate percentages. Remember that each square represents 1%.
| Interval | Sum | Percentage |
|---|---|---|
| One standard deviation of the mean | 34+34 | 68% |
| Two standard deviations of the mean | 13+34+34+13 | 94% |
| Three standard deviations of the mean | 2+13+34+34+13+2 | 98% |
In normal distribution about 68% of the data lies within σ, about 94% within 2σ, and about 98% within 3σ of the mean.