Confidence interval of product of two predictions

Let's say I make a prediction for a number of clouds per day which pass over an area. It comes with 95% confidence intervals [cloud low, cloud high]

Then let's say I make a prediction for the mean amount of water per day which passes over that area in the clouds. It comes with 95% confidence intervals [mean low, mean high]

To get the total water per day, I have to multiply the mean per day * the number of days.

Should I then multiply the confidence intervals [mean low * cloud low, mean high * cloud high], to get the confidence interval of the product?

• What do you suppose or know about the relationship between water content of clouds and number of clouds? For instance, is it possible that when more clouds are sighted they tend to be smaller (have less water)?
– whuber
Commented Nov 21, 2019 at 15:48
• More clouds implies more water. Assume clouds are identical in size, and carry the same amount of water per cloud. Commented Nov 21, 2019 at 15:53