Question
In: Statistics and Probability
In a backyard vineyard in Napa Valley with 10 grape vines in a row, if the...
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=700, p=0.6. In a drought the yield is Binomial with N=720 and P=0.5, while if the year is too wet, the yield of useful grapes per vine is N=650, P=0.65. Under climate change the probability of just the right year is about 0.4 of a too wet year is 0.1, and a dry year is 0.5. On a just right year the wine can sell for 120 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 20 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 4210 grapes. Given this yield:
a) What is the probability that you will be able to sell for 120 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 20 dollars a bottle?
d) What is your expected revenue per bottle?
Solutions
orchestra answered 1 year agoRelated Solutions
In a backyard vineyard in Napa Valley with 10 grape vines in a row, if the...
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...
The Sander’s family owns a large grape vineyard in Jackson, Mississippi. The grape vines must be...
The Sander’s family owns a large grape vineyard in Jackson,
Mississippi. The grape vines must be sprayed at the beginning of
the growing season to protect against various insects and diseases.
Two new insecticides have just been marketed: Pernod 5 and Action.
To test their effectiveness, three long rows were selected and
sprayed with Pernod 5 and three other were sprayed with Action.
When the grapes ripened, 400 of the vines treated with Pernod 5
were checked for infestation. Likewise,...
The Damon family owns a large grape vineyard in western New York along Lake Erie. The...
The Damon family owns a large grape vineyard in western New York
along Lake Erie. The grapevines must be sprayed at the beginning of
the growing season to protect against various insects and diseases.
Two new insecticides have just been marketed: Pernod 5 and Action.
To test their effectiveness, three long rows were selected and
sprayed with Pernod 5, and three others were sprayed with Action.
When the grapes ripened, 400 of the vines treated with Pernod 5
were checked...
The Damon family owns a large grape vineyard in western New York along Lake Erie. The...
The Damon family owns a large grape vineyard in western New York
along Lake Erie. The grapevines must be sprayed at the beginning of
the growing season to protect against various insects and diseases.
Two new insecticides have just been marketed: Pernod 5 and Action.
To test their effectiveness, three long rows were selected and
sprayed with Pernod 5, and three others were sprayed with Action.
When the grapes ripened, 425 of the vines treated with Pernod 5
were checked...
The Damon family owns a large grape vineyard in western New York along Lake Erie. The...
The Damon family owns a large grape vineyard in western New York
along Lake Erie. The grapevines must be sprayed at the beginning of
the growing season to protect against various insects and diseases.
Two new insecticides have just been marketed: Pernod 5 and Action.
To test their effectiveness, three long rows were selected and
sprayed with Pernod 5, and three others were sprayed with Action.
When the grapes ripened, 425 of the vines treated with Pernod 5
were checked...
The Damon family owns a large grape vineyard in western New York along Lake Erie. The...
The Damon family owns a large grape vineyard in western New York
along Lake Erie. The grapevines must be sprayed at the beginning of
the growing season to protect against various insects and diseases.
Two new insecticides have just been marketed: Pernod 5 and Action.
To test their effectiveness, three long rows were selected and
sprayed with Pernod 5, and three others were sprayed with Action.
When the grapes ripened, 390 of the vines treated with Pernod 5
were checked...
The Damon family owns a large grape vineyard in western New York along Lake Erie. The...
The Damon family owns a large grape vineyard in western New York
along Lake Erie. The grapevines must be sprayed at the beginning of
the growing season to protect against various insects and diseases.
Two new insecticides have just been marketed: Pernod 5 and Action.
To test their effectiveness, three long rows were selected and
sprayed with Pernod 5, and three others were sprayed with Action.
When the grapes ripened, 440 of the vines treated with Pernod 5
were checked...
The Damon family owns a large grape vineyard in western New York along Lake Erie. The...
The Damon family owns a large grape vineyard in western New York
along Lake Erie. The grapevines must be sprayed at the beginning of
the growing season to protect against various insects and diseases.
Two new insecticides have just been marketed: Pernod 5 and Action.
To test their effectiveness, three long rows were selected and
sprayed with Pernod 5, and three others were sprayed with Action.
When the grapes ripened, 440 of the vines treated with Pernod 5
were checked...
The Damon family owns a large grape vineyard in western New York along Lake Erie. The...
The Damon family owns a large grape vineyard in western New York
along Lake Erie. The grapevines must be sprayed at the beginning of
the growing season to protect against various insects and diseases.
Two new insecticides have just been marketed: Pernod 5 and Action.
To test their effectiveness, three long rows were selected and
sprayed with Pernod 5, and three others were sprayed with Action.
When the grapes ripened, 400 of the vines treated with Pernod 5
were checked...
You own a 10-acre vineyard and earn income by selling your grapes to wineries. Your vineyard...
You own a 10-acre vineyard and earn income by selling your
grapes to wineries. Your vineyard is currently planted to Merlot
grapes, but you are thinking of replanting with Syrah grapes
because they are commanding a higher market price per ton. Merlot
fetches $1600 per ton but Syrah sells for $2800 per ton, those
prices are expected to remain stable, and you produce 50 tons per
year. Either way, you plan to sell the vineyard 5 years from today
(at...
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