Final answer:
The z-score represents the number of standard deviations a data point is from the mean. To calculate the percentages for a z-score of -1.61 with a given tail percentage, subtract the tail percentage from 100% for scores above the z-score, subtract half the tail percentage from 50% for scores between the mean and the z-score, and subtract the percentage below the z-score from 100% for scores above a specific z-score.
Step-by-step explanation:
The z-score represents the number of standard deviations a data point is from the mean in a normal distribution. For a z-score of -1.61, we can use a standard normal distribution table to find the probabilities:
a. To find the percentage of scores above the z-score, we subtract the tail percentage from 100%. In this case, it would be 100% - 5.37% = 94.63%.
b. To find the percentage of scores between the mean and the z-score, we subtract the percentage below the z-score from 50%. In this case, it would be 50% - (5.37%/2) = 48.315%.
c. To find the percentage of scores above a z-score of 1.61, we subtract the percentage below the z-score from 100%. In this case, it would be 100% - (100% - 5.37%) = 5.37%.