Question

In a backyard vineyard in Napa Valley with 10 grape vines in a row, if the weather works well (just right), rain in the Spring and dry through summer, the yield for each vine is distributed roughly binomial with N=800, p=0.5. In a drought the yield is Binomial with N=800 and P=0.48, while if the year is too wet, the yield of useful grapes per vine is N=600, P=0.2. Under climate change the probability of just the right year is about 0.2 of a too wet year is 0.1, and a dry year is 0.7. On a just right year the wine can sell for 100 dollars/bottle, on a dry year the quality drops so it will sell for 60 dollars a bottle, on wet year it will sell for 30 dollars a bottle (For a Z score with absolute value >5 assume the probability is 0) The yield for all 10 vines was more than 3900 grapes. Given this yield:

a) What is the probability that you will be able to sell for 100 dollars a bottle?

b) What is the probability that you will be selling for 60 dollars a bottle?

c) What is the probability that you can only sell for 30 dollars a bottle?

d) What is your expected revenue per bottle?

Answer 1