For a particular value, this table gives the percent of scores between the mean and the z-value of a normally distributed random variable. What percent of the total population is found between the mean and the z-score, assume z = 2.79

.4974

Right!

To find the percent of the total population between the mean and a given z-score, we need to use the standard normal distribution table (also known as the z-table) or a statistical calculator.

The standard normal distribution table provides the area/probability values for different z-scores. A z-score of 2.79 corresponds to a specific area under the curve. We can find this area by referring to the standard normal distribution table.

1. Begin by finding the absolute value of the z-score. In this case, the absolute value of 2.79 is 2.79. This step is necessary because the standard normal distribution table only provides positive z-scores.

2. Locate the z-score in the leftmost column of the table. The digits before the decimal point represent the whole number part, while the digits after the decimal point represent the first decimal place. For example, a z-score of 2.7 will be located in the row with the whole number 2 and the column labeled 0.07.

3. Find the column corresponding to the second decimal place. In this case, the column with 0.09.

4. Intersection of the row and column from steps 2 and 3 will give the area/probability value associated with the z-score. Let's say the value is X.

5. Since we are interested in the percentage of the total population between the mean and the z-score, we need to convert the probability to a percentage value by multiplying X by 100%.

Therefore, by using the standard normal distribution table or calculator, find the corresponding area/probability value for a z-score of 2.79 and convert it to a percentage to determine the percent of the total population between the mean and the z-score.