Question 864853: In a certain distribution of numbers, the mean is 80 and the standard deviation is 8. At least what fraction of the numbers are between 56 and 104? Give answers as common fractions reduced to lowest terms.
PLEASE HELP!!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Notice how 80 - 3*8 = 56 and 80 + 3*8 = 104. So 56 is 3 standard deviations below the mean and 104 is 3 standard deviations above the mean.
The interval we're focusing on is basically all the values that are within 3 standard deviations of the mean.
So we use the empirical rule and we see that roughly 99.7% of the population is within 3 standard deviations of the mean.
If you want that as a fraction, then this is where it gets tricky. The reason why is because 99.7% or 0.997 is an approximation and the approximation is very rough.
A better approximation is 0.9973002, and an even better approximation is 0.997300203936740, and so on.
This decimal expansion goes on forever without a predictable pattern.
So essentially this number is NOT rational and cannot be written perfectly as a fraction. If you really want a fraction (it's not advisable really), then you could stick with 99.7% and write that as 99.7/100 = 997/1000. That's probably the most intuitive way to do it.
|
|
|
