DEALING WITH NORMAL DATA AND ZSCORES - Statistics Project ExampleThe average current test score of the students is 82.06 and varies from the mean by about 9.05. The z-score of the students’ test grades can be calculated using below formula:Table 1 shows the student’s z-scores for their previous and current test grades. The maximum and minimum z-scores for the previous test score are 1.48 and -1.54, respectively. The maximum and minimum z-scores for the current test score are 1.76 and -1.55, respectively. Thus, there is no outlier in both the current and previous test scores as all the z-score values are in between -3 and +3. A total of 9 students’ z-score decreased from the previous test to current test and a total of 9 students’ z-score increased from the previous test to current test. The theoretical normal distribution probability of a z-score below 0.50 is about 0.6915. The number of students whose z-score is below 0.50 in current score is 11. Thus, proportion of the students test scores on the current test only fall below z = .50 is about 0.6111 which is very close to the theoretical normal distribution
