Let's say, I've a table with a list of trips I need to make this week and I want to calculate a confidence interval for the average trip duration time for all the trips I'll make in the week.
| Var | Trip name | mean (minutes) | std (minutes) | Trips scheduled |
|---|---|---|---|---|
| A | Home-University | 15 | 3 | 5 |
| B | University-Home | 19 | 4 | 3 |
| C | University-Work | 5 | 1 | 2 |
| D | Work-Home | 20 | 7 | 2 |
I know that
E[X+Y] = E[X] + E[Y]
And Var[X+Y] = Var[X] + Var[Y]
So the average trip duration given the data in the table must be: $$ \mu_{trip\ duration} = \frac{5(A.mean) + 3(B.mean) + 2(C.mean) + 2(D.mean)}{12}$$
And a similar formulation for the variance, but If I want to create a confidence interval should I assume that this distribution (the sum of all the trips) follows a normal distribution and then multiply the standard error by the z-score? or is it wrong to assume a normal distribution?