A sample of n=20 has a mean of M = 40. If the standard deviation is s=5, would a score of X= 55 be considered an extreme value? Why or why not?
I understand that the score in question is 3 standard deviations above the mean. But I thought that I would need to convert this to a z score to determine whether it was extreme, but when I do, I get a z score of 3 and I can find that on the unit normal table...but I don't know how to determine whether my score is in the body or the tail. Am I on the right path? I'm really trying here.
The scores in the "smaller portion" would tell you how extreme the score is.
The scores in the "smaller portion" in the table would tell you how extreme the score is.
You're on the right track! To determine whether a score is considered extreme, you should indeed convert it to a z-score. The z-score tells you how many standard deviations a particular score is away from the mean.
In this case, the score of X=55 has a z-score of 3, as you correctly calculated. To determine whether this score is considered extreme, you need to check whether it falls in the body or the tail of the standard normal distribution.
In a standard normal distribution, approximately 99.7% of the data falls within 3 standard deviations of the mean. More specifically, about 68% falls within 1 standard deviation, about 95% falls within 2 standard deviations, and about 99.7% falls within 3 standard deviations.
Since your score of X=55 corresponds to a z-score of 3, which is 3 standard deviations above the mean, it falls in the extreme tail of the distribution. This means that a score of 55 would be considered an extreme value in this case.
To summarize, a score is considered extreme if it falls in the tail of the distribution, beyond a certain number of standard deviations from the mean. In this case, a score of X=55 with a z-score of 3 is considered extreme since it falls 3 standard deviations above the mean.
I hope this explanation helps! Let me know if you have any further questions.