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Setler [38]
2 years ago
14

Dairy farmers are aware there is often a linear relationship between the age, in years, of a dairy cow and the amount of milk pr

oduced in gallons per week The least squares regression line
produced from a random sample is Milk = 40.8 – 1.1 (Age). Based on the model, what is the difference in predicted amounts of milk produced between a cow of 5 years and a cow of 10 years?

A cow of 5 years is predicted to produce 5.5 fewer gallons per week

B A cow of 5 years is predicted to produce 5.5 more gallons per week

c) A cow of 5 years is predicted to produce 1.1 fewer gallons per week

D) A cow of 5 years is predicted to produce 1.1 more gallons per week

A cow of 5 years and a cow of 10 years are both predicted to produce 40.8 gallons per week
Mathematics
1 answer:
Jobisdone [24]2 years ago
6 0

Answer:

B. A cow of 5 years is predicted to produce 5.5 more gallons per week.

Step-by-step explanation:

Let M(a) = 40.8-1.1\cdot a, where a is the age of the dairy cow, measured in years, and M(a) is the predicted milk production, measured in gallons per week.

Besides, we consider a_{1} and a_{2}, such that a_{1}\ne a_{2}, we define the difference between predicted milk productions (\Delta M) below:

\Delta M = -1.1\cdot (a_{2}-a_{1}) (1)

If we know that a_{1} = 5\,yr and a_{2} = 10\,yr, then the difference between predicted milk productions is:

\Delta M = -1.1\cdot (10-5)

\Delta M = -5.5\,\frac{gal}{week}

That is, a cow of 5 years is predicted to produce 5.5 more gallons per week than a cow of 10 years. Hence, the right answer is B.

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