Final Answer:
99.7% percent of the data lies outside of three standard deviations of the mean, thus the correct option is c.
Explanation:
68% of the data lies within three standard deviations of the mean. This means that the remaining 32% of the data lies outside of three standard deviations of the mean. That data is split equally between the two sides of the mean, so 16% of the data lies outside of three standard deviations in both the positive and negative directions. To calculate the percentage of data that lies outside of three standard deviations of the mean, we must double the 16%. This results in 32%, which when rounded to the nearest tenth is 99.7%.
Standard deviation is a measure of how spread out numbers are in a data set. It is calculated by taking the square root of the variance. A standard deviation of one means that 68% of the data lies within one standard deviation of the mean. When the standard deviation is increased to three, it means that 99.7% of the data lies within three standard deviations of the mean. This is calculated by taking the area under the normal curve which represents the data and multiplying it by three.
The normal curve is a bell-shaped graph that represents the data in the form of a probability distribution. It is used to calculate the probability of certain events occurring, and it is used to determine the area under the curve in order to calculate the percentage of data that lies within or outside of a certain number of standard deviations from the mean.
In conclusion, 99.7% of the data lies outside of three standard deviations of the mean. This is calculated by doubling the 16% of the data that lies outside of three standard deviations and rounding the result to the nearest tenth. This is done by taking the area under the normal curve which represents the data and multiplying it by three.