The objective of this case study is to demonstrate a very direct representation of how one translates uncertainties into distributions.

My friends ran some baseline figures to estimate the costs of laundry when done in town. They had just done their first hand-washed load and wanted to understand how much of a cost savings it could be. They posted this to their Instagram story.

### Four to six loads of laundry per month.

### Each load costs between $2.75 and $3.75.

Using these two distributions, we analyze the cost of laundry under uncertainty.

### The distance to town varies quite a bit, but we try to stay close.

### Gas prices are reasonable, but do vary depending on where we are.

### Fuel economy of the truck varies with incline and elevation.

Now we have a summary of getting to and from town.

Adding these two together, we get a summary of the total potential costs.

## Summary

Our model given the specified uncertainties predicts that the average cost to Gabbi and Govinda will be $20 per month. Their guesstimate of $15 appears to be on the very optimistic side of the equation.

Since the gas price estimate was pretty close, this one likely comes down to the machine cost. They figured $10, which reflects a $2.50 machine load, which is cheaper than any I've seen in Denver.

So hopefully this was a useful case study for them, since it highlights just how expensive laundromats can be for them on the road, further incentivizing them to hand-wash when they can. It is more dramatic a difference than they even realized!

That's why it's important to

*Mind the Math*