To get the area between two z- scores, tell Excel to subtract The area to the left of the higher z-score, minus the area to the left of the lower z-score. “Find the total area under the normal curve.”

The total area under the curve must equal 1. Every point on the curve must have a vertical height that is 0 or greater. (That is, the curve cannot fall below the x-axis.) Because the total area under the density curve is equal to 1, there is a correspondence between area and probability.

tails

The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon. The area of the shaded part can occur in two ways in polygons. The shaded region can be located at the center of a polygon or the sides of the polygon.

If the z-score is positive, then the body will be the area that is below that z-score, and the tail will be the area that is above that z-score. If the z-score is negative, then the body will be the area that is above that z-score, and the tail will be the area that is below that z- score.

A negative z-score reveals the raw score is below the mean average. For example, if a z-score is equal to -2, it is 2 standard deviations below the mean. Another way to interpret z-scores is by creating a standard normal distribution (also known as the z-score distribution or probability distribution).

Area Between Two Negative z Scores Use the standard normal distribution table to look up the areas that go with the two corresponding positive z scores. Next, subtract the smaller area from the larger area. For example, finding the area between z1 = -2.13 and z2 = -. 45, is the same as finding the area between z1* = .

approximately 68 percent

The standard score (more commonly referred to as a z-score) is a very useful statistic because it (a) allows us to calculate the probability of a score occurring within our normal distribution and (b) enables us to compare two scores that are from different normal distributions.

Lower z-score means closer to the meanwhile higher means more far away. Positive means to the right of the mean or greater while negative means lower or smaller than the mean. A negative z-score reveals the raw score is below the mean average. …

If a z-score is equal to 0, it is on the mean. If a Z-Score is equal to +1, it is 1 Standard Deviation above the mean. If a z-score is equal to +2, it is 2 Standard Deviations above the mean. This means that raw score of 98% is pretty darn good relative to the rest of the students in your class.

1. An extreme score happens when z value is above 2 or below -2.

Extreme scores are the lowest and highest possible scores for persons on items, or for items by persons. They include zero and perfect scores. They are shown in the Tables as MINIMUM ESTIMATE MEASURE and MAXIMUM ESTIMATE MEASURE.

The values for z range from zero to infinity.

Remember, z = 0 is in the center (at the mean), and the extreme tails correspond to z-scores of approximately –2.00 on the left and +2.00 on the right. Although more extreme z-score values are possible, most of the distribution is contained between z = –2.00 and z = +2.00.

Z-scores are also known as standardized scores; they are scores (or data values) that have been given a common standard. This standard is a mean of zero and a standard deviation of 1. Contrary to what many people believe, z-scores are not necessarily normally distributed.

Note the parentheses! Data that is two standard deviations below the mean will have a z-score of -2, data that is two standard deviations above the mean will have a z-score of +2. Data beyond two standard deviations away from the mean will have z-scores beyond -2 or 2.