Question 303:

Asked on August 1, 2008

1

Answer:

No answer provided yet.

You're right, if you don't have the mean or standard deviation you can't calculate a z-score from a single data-point. However, if by 100, that person was referring to 100%, then you can lookup what z-score corresponds to 100% of the area under the normal curve. You could do this in fact for any percentage from 0 to 100 inclusive (like 20%, 50% 77%, 91.654% etc) using the percentile to z-score calculator .

Since the area under a normal curve can be divided into an infinite number of smaller and smaller pieces, all adding up to 1 or (100% of the area) the values 0 and 100 would both have z-scores of -infinity and infinity. That's because the tails of the normal curve stretch out to infinity in each direction.  So the answer mathematically to what is the z-score of 100% is infinity, again only if your asking about percentage and not some raw score.

Since infinity does not always work well in practical applications, many people will stop the z-score at 6 or 7, which is not 100%, but 99.9999997958 and 99.9999999997 of the area.