Help with standard deviations, means, distributionsI am confused about comparing data by looking at the mean and standard deviation. Example shows...

Group A

The mean 100 out of
120 with SD=5 means that in general the variabilities of data in the population is 100 +
or - 5. Thus, data in this population range from 95 -
105.

Group B

The mean 85 out
of 120 means that in general the variabilities of data in the population is 85 + or -
10. Thus, data in this population range from 75 - 95

In
group A, from the question we know that there is a person score 90 out of 120. It means
that there is a score that not in the range 95 - 105. This data is an outlier. Data with
an outlier cannot have a normal distribution.

There is not
enough information to make a decision about distribution in group B. However, if assumed
that the case of this person is turn into group B. We can see that the 90 out of 120 is
in the range of 95 - 105. Thus, data in group B has a normal
distribution.

If a person reach 90 out of 120 in group A,
it means that this person did worse on the test, because his/her score falled into lower
than the lowest average, which is 95. However, if this person is in group B, he/she did
fair on the test because his/hert grade is in the mid of range 95 -
105.

I hope this answer can help
you.