Estimate the storage capacity of a 20-minute-vinyl in bits.
We should estimate since it depends on a lot of factors but I have no clue how to approximate/estimate the amount of bits that can be stored on a 20-minutes-vinyl. How would you estimate the storage capacity? The exercise is more about reasoning and less about how many bits a 20-minutes-vinyl can actually store.
Assuming you're talking about the old LP (or SP) records, the basic idea is this:
It was a single groove cut into the vinyl spiralling towards the center, which is how the stylus followed it. Hence the storage capacity needs to take into account:
The length of the groove (which can be calculated by the diameter of the record's playing surface and the distance between points on adjacent groove sections;
The number of "digits" that can be stored per distance in the groove; and
The number of values each digit can have (i.e., distinguishable groove depths).
So, for example (you will need to figure out your own figures), let's say there are two distinguishable depths in the groove (shallow and deep). Further assume that 1,000 "digits" can be stored per linear meter, and that the total groove length is 40m.
The storage capacity would then be 40,000 bits.
Another approach where you have only the time and cannot easily get the groove length, is to use different figures.
For example, assume that decent music will have different possible frequency/volume pairs (at 8 bits each) and that you need sixty of these per second to get a decent sound quality. That would be 16 * 60 = 960 bits per second, which would give you a capacity of 1,152,000 bits for a 20-minute duration.
Just remember those are example values, the actual values may be far different in reality. But, since you've stated the intent here is just to demonstrate estimation skills, that should be okay.