Question

In finding the areas under the normal curve, if we wish to determine the area between A and B, and both A and B are greater than the mean (with A further away from the mean than B)

a)We find the area between the mean and A and subtract the area between the mean and B

b)We find the area between the mean and A and add the area between the mean and B

c)We find the area between the mean and A and subtract it from .50

d)We find the area between the mean and A and add it to .50

Answer 1

a.

Explanation:

A and B both are greater than mean and so A and B lies on the right side of mean. Further it is stated that A is more away from the mean than B. It means that A is greater than B. So, in order to find the area between A and B we have to subtract the area of mean to B from area of mean to A. It can be explain in the notations as

P(B<X<A)=P((B-μ)/σ<z<(A-μ)/σ)

P(B<X<A)=P(z<(A-μ)/σ)-P(z<(B-μ)/σ)

Hence, we find the area from mean to A and subtract the area from mean to B.