Inverse Normal Distribution Problems: Find Z-Scores for Given Cumulative Percentages

Question

4) If you have 20% of your data lying below a z-score, what is that z-score? 5) If you have 34.5% of your data lying above a z-score, what is that z-score?

Accepted Answer

4) $z \approx -0.84$; 5) $z \approx 0.39$

Answer

Step 1: For question 4, we need the z-score where the cumulative area to the left is 0.20 (20%). Use a standard normal table or inverse normal calculator to find the z-score corresponding to an area of 0.20, which is approximately -0.84. Step 2: For question 5, first find the cumulative area to the left of the z-score: 1 - 0.345 = 0.655 (since 34.5% is above the z-score). Use a standard normal table or inverse normal calculator to find the z-score corresponding to an area of 0.655, which is approximately 0.39.