Income percentile ranks are numbers from 0 to 100 that indicate where you sit in the income distribution - for example, 75 would mean you earn more income than three quarters of people, but less than the top quarter. Let's assume a child's expected income percentile is a linear function of their parents' income percentile. It turns out the intercept is enough to pin down the slope. Do you see why? If the intercept is 20 - which means the lowest-income parents have children who end up at the 20th percentile, on average - what is the slope?

This problem is from an app called probability puzzles.

My approach: I realised $y=ax+b$ could be the line for child but we don't have any information about the slope. We know that percentile is uniformly distributed between 0 and 100 so expected value is 50 but I don't see how to proceed from here.

This problem is from an app called probability puzzles.

My approach: I realised $y=ax+b$ could be the line for child but we don't have any information about the slope. We know that percentile is uniformly distributed between 0 and 100 so expected value is 50 but I don't see how to proceed from here.