Consider the following. (Give your answers correct to two decimal places.)

(a) Find the standard score (z) such that the area above the mean and below z under the normal curve is 0.3989.


(b) Find the standard score (z) such that the area above the mean and below z under the normal curve is 0.4875.


(c) Find the standard score (z) such that the area above the mean and below z under the normal curve is 0.3628.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.3989, .4875, .3628) related to your Z scores.

I still do not understand how you get the answer of above or below??

Find the area under the standard normal curve to the left of z = −1.5 and to the right of z = −1.Round your answer to four decimal places, if necessary.

To find the standard score (z) for a given area under the normal curve, we can use a standard normal distribution table or a statistical calculator. Here's how you can find the answers to each question:

(a) To find the standard score (z) for an area of 0.3989, we want to find the z-value that corresponds to an area below it in the normal distribution curve. By looking up the area of 0.3989 in the standard normal distribution table (also known as the z-table), we find that the corresponding z-value is approximately 0.25.

(b) Similarly, to find the standard score (z) for an area of 0.4875, we look up this area in the z-table. The corresponding z-value is approximately 0.98.

(c) To find the standard score (z) for an area of 0.3628, we can use the z-table again. The closest area we find in the table is 0.3621, which corresponds to a z-value of approximately -0.37 (Note that the z-values in the table are usually given up to two decimal places).

So, the answers are:
(a) z ≈ 0.25
(b) z ≈ 0.98
(c) z ≈ -0.37