Final answer:
In a public school examination with mean marks of 40% and a standard deviation of 20%, we can calculate the pass marks before and after moderation. The pass marks before moderation were 35% and after moderation they were 50.4%.
Step-by-step explanation:
To find the pass marks before and after the moderation, we need to understand the normal distribution of marks. In a normal distribution, the mean is the center of the distribution and the standard deviation measures the spread of the marks. Given that 60% of the students failed, we can find the z-score corresponding to this percentage. Using a standard normal distribution table or a calculator, we find that the z-score for 60% is approximately -0.25.
Now, we can use the z-score formula, z = (x - mean) / standard deviation, to find the pass marks before moderation. Rearranging the formula, x = z * standard deviation + mean, we substitute the values: x = -0.25 * 20 + 40 = 35. Hence, the pass marks before moderation were 35%. After moderation was done and 70% of the students passed, we can find the z-score corresponding to this percentage, which is approximately 0.52. Substituting the values into the formula, x = 0.52 * 20 + 40 = 50.4. Therefore, the pass marks after moderation were 50.4%.