For a normal distribution, what is the probability that the data falls somewhere .5 standard deviations from the mean?
1 Answer
Explanation:
For a normal distribution, if we are using the standard normal distribution
This question is asking about the area under the normal distribution curve between the z-scores of -0.5 and +0.5. This can be done one of two ways. EIther you can find a z-score table which provides things known as cumulative from the mean areas, or you can use a regular z-score table (cumulative).
In the latter case, you have to be clever; you look up the +0.5 z-score, find that probability, and then subtract the -0.5 z-score value from the same table. This is because we are only interested in the amount between those z-score values, while cumulative z-score tables gives us the probability from
z-score +0.5: 0.6915
z-score -0.5: 0.3085