You breed miniature mules (father is a miniature donkey, mother is a miniature horse) and currently have as breeding stock 1 jack (male donkey) and 7 mares (female horses) and these are able to produce 7 mule foals (baby mules) for you every year. You would like to produce miniature mules that are quite small, but unfortunately there is considerable variation in the sizes of mule offspring produced even from the same set of parents. Based on the best information you can obtain, the heights of the mules you produce are normally distributed with a mean height of 32.5 inches and a standard deviation of 1.25 inches. Any mule less than or equal to 32 inches can be sold for a high price and any mule greater than 32 inches in height can be sold only for a lower price.
If a mule foal is both less than 32 inches in height and of a desirable color it can be sold for a very high price. You have determined that there is a 20% probability that any given foal will be of a desirable color, and that color is independent of height. What is the probability that you will have at least one mule that can be sold for a very high price in any given year?
phi((x - avg)/(std dev.))
phi((x + .5 - np)/(sqrt(np(1 - p))))
The Attempt at a Solution
I know the probability of any given mule being sold at a high price when it's less than 32 inches. I just don't know what to do with the other probability that's given in the question. What's the correct formula to use or start with? I just need a point in the right direction.