SOLUTION: The probability of a given score range is 0.4893. The bottom of the score range is the average (z=0). What is the z-score for the upper end of the distribution

Question 1099079: The probability of a given score range is 0.4893.
The bottom of the score range is the average (z=0).
What is the z-score for the upper end of the distribution
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i think you are looking for the z-score which has an area of .4893 between the mean and it.

since the normal distribution is symmetric about the mean, this mean that the z-score will have .4893 + .5 = .9893 area of the distribution curve to the left of it.

that would correspond to a z-score of 2.301

the following pictures show you what i mean.

the first picture shows that the z-score that has an area of .9893 to the left of it is 2.301.

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the second picture shows that if you enter the z-score of 2.301 and ask for the area to the left of it, that area will be .9893.

$$$$

the third picture shows that if you enter the z-score of 2.301 and ask for the area between the mean (z-score of 0) and the z-score of 2.301, that area will be .4893.

$$$$

note that the first picture is looking to find the z-score from a given area, so you select the "value from an area" option.

note that the second and third picture is looking to find the area from the given z-score, so you select the "area from a value" option.

this particular z-score calculator can be found at http://davidmlane.com/hyperstat/z_table.html
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