(Use Bayes Rule) 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 the summer, the yield for each vine is distributed roughly binomial with N=800, p=.8 . In a drought the yield is binomial with N=900 and P=.6, while if the year is too wet, the yield of useful grapes per vine is N=700, P=.85. Under climate change the probability of a just right year is about .15, of a too wet year is .15, and a dry year is .7. On a just right year the wine can sell for 200 dollars/bottle, on a dry year the quality drops so it will sell for 100 dollars a bottle, on a wet year it will sell for 25 dollars a bottls. (For a Z score with absolute value greater than 5, assume the probability is 0). a. The yield for all 10 vines was more than 6350 grapes. Given this yield: i. What is the probability that you will be able to sell for 200 dollars a bottle? (Hint: break it down, given the information, what is the probability of 6350 or more from 10 vines, given a just right year, a dry year, or a wet year.) ii. What is the probability that you will be selling for 100 dollars a bottle? iii. What is the probability that you can only sell for 25 dollars a bottle? iv. What is your expected revenue per bottle?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
(Use Bayes Rule) 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 the summer, the yield for each vine is distributed roughly binomial with N=800, p=.8 . In a drought the yield is binomial with N=900 and P=.6, while if the year is too wet, the yield of useful grapes per vine is N=700, P=.85. Under climate change the
a. The yield for all 10 vines was more than 6350 grapes. Given this yield:
i. What is the probability that you will be able to sell for 200 dollars a bottle? (Hint: break it down, given the information, what is the probability of 6350 or more from 10 vines, given a just right year, a dry year, or a wet year.)
ii. What is the probability that you will be selling for 100 dollars a bottle?
iii. What is the probability that you can only sell for 25 dollars a bottle?
iv. What is your expected revenue per bottle?
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