Standard Deviation

Question

In a distribution where the mean is 60 and the standard deviation is 2, find the largest fraction of the numbers that could meet the requirements of less than 56 or more than 64. Of the numbers in the distribution, the fraction that is less than 56 or more than 64 is at most what?

Answer 1

If the data is normally distributed, then draw a picture, draw a picture, draw a picture.

 

Draw a normal distribution

label the mean

label + 1 and -1 standard deviations, 68% of the data will be between 58 and 62 because the standard deviation is 2.

 

Next label +2 and -2 standard deviations. 95% of the data will be between 56 and 64 because if the data in normally distributed then 95% of the data will be within 2 standard deviations from the mean.

 

The question is calling for the percent of data that IS NOT between 56 and 64, so that will be the 5% that is not between 56 and 64.

 

This explanation should make sense if you are looking at a labeled normal distribution.