For a standard normal distribution, how do you find the percentage of data that are between 3 standard deviations below the mean and 1 standard deviation above the mean?
1 Answer
It's about 84%.
Explanation:
You could use a TI 80-series calculator under the "DISTR" menu to get the answer.
Once there, enter: normalcdf(-3,1,0,1)
The last two numbers "0" and "1" refer to using the "standard normal distribution" with a mean of 0 and a standard deviation of 1...this should be used whenever your measurement units are "number of standard deviations". The "-3" represents 3 standard deviations below the mean in this situation and the second number, the first "1", represents 1 standard deviation above the mean in this situation.
The calculator should return an answer of .8399947732, which rounds to .84 = 84%.
The "68-95-99.7" rule can also be used. This says that about 68% of the data will be within 1 standard deviation of the mean; about 95% of the data will be within 2 standard deviations of the mean; and about 99.7% will be within 3 standard deviations of the mean. This leads us to conclude about 99.7/2 = 49.85% of the data is between 3 standard deviations below the mean and the mean, while about 68/2 = 34% are between the mean and 1 standard deviation above the mean. Adding these together gives about 84%.
