How much time is spent waiting per day for a real human in the Automated Systems in the US?

I: So what we want to know is how many people spend time waiting on the phone to talk to a real human. And this would include going through the prompts and all? I would say we should include it because from a user standpoint, as soon as that number dials I want to get to a human so even the time I spend selecting options is something that's counting against my time and is making me feel omg! it's taking so long to get to a human. This is also why the best companies spend money on best Speech Recognition programs and best IVR experience, etc. 

Interveiwer: Good point! Let's go with your assumption.

I: Ok. I think I will take a top down approach whereby let's start with # of US population and then estimate how many people may call automated systems. But some actually just leave a phone number to get a call back instead of waiting for human on hold. Some also spend less time while some spend more time on phone waiting since queue is always different. Also, let's not estimate what happens after a major disaster because insurance company hold times and evne telecom company hold times, etc. increase significantly during those times. 

Interviewer: Sounds like a fine approach. 

I: Great! So we have 360M people in US. If we include any type of businesses as well as calls made to government agencies and assuming most calls are made during workhours by working people, it's safe to assume that 40% of people call support / customer service. 40% may seem low but I also assumed that these days companies have made it nearly impossible to find phone #s so most people quit looking for ph# and I also know many who won't for some reason pick up the phone and call help / support # (blows me). + These days ton of support is provided using AI either by product just telling you what is potentially wrong and attempting to fix it by itself or by an AI chat bot. 

40% of 360M = 144M 

Out of 144M people, since most people are working during the normal business hours, prob prefer to get a call back since they don't want to be seen holding on a phone for long. So let's assume about 70% choose that option. 70% of 144M = 100.8M, 30% of 144M = 43.2M.

If we include experience immediately after you dial a number, most companies have 3 layers deep options and each layer has about 5 different options to choose from. I could break it down by x % have 3 optiosn per layer , while x% has 10 options at each layer, etc. but that is too detailed for now. Each layer choices take about 1 min so that's 3 min of option choosing which sounds about right. 

Those who choose to just get a call back still have to go through option choosing so they still spend 3 min for that and 1 extra min after they get a call back. So that's 100.8M * 4 min = 403.2M minutes / 60 min an hour = 6.72M hours.

Out of the 30% who stay on the phone go who through 3 min of dialing options, 70% spend good 7 min, 20% spend 10 min, 10% spend 15 min. 

70% * 43.2M = 30.24M * (7+3) = 302.4M min / 60 min an hour = 5.04M hours

20% of 43.2M = 8.64M * (10 + 3) = 112.32M min / 60 min an hour = 1.87M hours

10% of 43.2M = 4.32M * (15 + 3) = 77.76M min / 60 min an hour = 1.3M hours 

So 6.72M hours + 5.04M hours + 1.87M hours + 1.3M hours = 14.93M hours of waiting on the phone. 

Wow! that number seems quite high. Let's say we have 360M people each having 24 hours results to 150M hours each day over 360M people. 14.93M hours / 150M hours = .09 = 9% of the total time spent on phone waiting for a human. That doesn't seem a whole lot so maybe my number is lower than what reality might be. I could add in variation to estimate those who end up spending 30 min to evne an hour sometimes but those are rare cases so it may just be like 5%. That won't really help bump up the numbers by that much. I don't know where else I could have gone wrong though.