We have no ideal on how to start this problem, we have look for it on the charts, did not see. Please help
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.
I think a visit to
http://davidmlane.com/hyperstat/z_table.html
will help a lot here.
I have looked at that page and really do not understand how to use it, it ask for mean, sd, below, above etc. Would you please just once show me how to plug the information into this graph and I also get mixed up on which one to use. It looks like it may help me if I just knew how to use it.
To solve these problems, we need to use the standard normal distribution table (also known as the Z-table). This table provides the area under the normal curve for different standard scores (z-scores).
(a) To find the standard score (z) such that the area above the mean and below z under the normal curve is 0.3989, we need to find the z-score that corresponds to an area of 0.6011 (1 - 0.3989) in the table.
Using the Z-table, locate the closest value to 0.6011. The closest value in the table is 0.6015, which corresponds to a z-score of 0.25. Therefore, the standard score (z) is 0.25.
(b) To find the standard score (z) such that the area above the mean and below z under the normal curve is 0.4875, we need to find the z-score that corresponds to an area of 0.5125 (1 - 0.4875) in the table.
Using the Z-table, locate the closest value to 0.5125. The closest value in the table is 0.5122, which corresponds to a z-score of 1.95. Therefore, the standard score (z) is 1.95.
(c) To find the standard score (z) such that the area above the mean and below z under the normal curve is 0.3628, we need to find the z-score that corresponds to an area of 0.6372 (1 - 0.3628) in the table.
Using the Z-table, locate the closest value to 0.6372. The closest value in the table is 0.6371, which corresponds to a z-score of 0.36. Therefore, the standard score (z) is 0.36.
Remember to round your answers to two decimal places, as specified in the question.