A homeowner has installed a new energy-efficient furnace. It is ...

[Bernana]

A homeowner has installed a new energy-efficient furnace. It is estimated that over a year the new furnace will reduce energy costs by an amount that can be regarded as a random variable with a mean of 265 and standard deviation of 55.
 
  Stating any assumptions you need to make, find the mean and standard deviation of the total energy costs reductions over a period of 5 years.

Question 2

If the coefficient of correlation is 0.75, what is the value of the coefficient of determination?
 
  A) 0.8660
  B) 0.5625
  C) 0.5916
  D) 0.6123

[debra928]

Answer to Question 1

Assume that costs are independent across years.
Let X = Energy costs reductions over a period of one year, and
Y = Energy costs reductions over a period of 5 years.
Then, Y = 5X. Hence, Y = 5X = (5 )(265 ) = 1325, and Y = 5X = (5 )(55 ) = 275.

Answer to Question 2

B