A family-owned sauces and spice company are trying to determine how long their flavor-packed spices will last for their customers. They are planning an online marketing and sales strategy and this would be helpful information.
People use widely different amounts per serving, and there is a bit of natural variation in the amount in each jar.
Mind the Math ran the numbers. Let's walk through them.
Each container is 4oz (113g). 5% relative uncertainty in the weight of each package translates to just around 5.5g as a margin of error. Since this uncertainty can go in either direction (over or under), that translates to an 11g variation, probably equivalent to a several servings.
The bigger variation will be in the amount people use.
Based on our experiments with usage, the median serving is about 2 grams. Some heavy users will use twice as much. Less than 1 gram is hardly perceptible. The distribution shown here is a suitable approximation for our purposes.
With all that said, here is the resulting chart of the number of servings. The number you might see on a label would be simply something like "60," but clearly there is a lot of variation.
How long will the spices last?
We now turn our attention to the implications for sustained re-orders. We know the product is amazing (we've been using it for lots of meals), but identifying the range of behaviors of our potential consumers can allow for better planning for marketing campaigns.
We assume that the customers of this product will use it between once every two weeks and five times a week. Anything in this range is treated as equally likely since we have no prior knowledge to tell us otherwise. We find that the distribution to be really spread out:
The most enthusiastic consumers can be expected to re-order every 2 months or so. This is a "best case"scenario that was identified for our client. The average user may order once or twice per year.