Predict the monthly heating bill for a house that has 2,600 square feet and has a heat pump that is nine years old.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Delmarva Power is a utility company that would like to predict the monthly heating bill for a household in Kent County during the month of January. A random sample of 18 households in the county were selected and their January heating bill recorded. This data is shown in the table below along with the square footage of the house (SF), the age of the heating system in years (Age,) and the type of heating system (heat pump = 1 or natural gas = 0).
|
Household |
Bill |
SF |
Age |
Type |
|---|---|---|---|---|
|
1 |
$255 |
2,070 |
7 |
Natural Gas |
|
2 |
$286 |
1,909 |
17 |
Natural Gas |
|
3 |
$296 |
2,004 |
8 |
Natural Gas |
|
4 |
$300 |
2,307 |
22 |
Natural Gas |
|
5 |
$305 |
3,021 |
5 |
Natural Gas |
|
6 |
$317 |
2,683 |
14 |
Natural Gas |
|
7 |
$321 |
1,511 |
8 |
Natural Gas |
|
8 |
$321 |
2,836 |
3 |
Natural Gas |
|
9 |
$339 |
2,553 |
20 |
Natural Gas |
|
10 |
$349 |
2,497 |
11 |
Natural Gas |
|
11 |
$369 |
2,103 |
12 |
Heat Pump |
|
12 |
$374 |
2,486 |
18 |
Heat Pump |
|
13 |
$381 |
2,279 |
19 |
Heat Pump |
|
14 |
$413 |
2,477 |
17 |
Heat Pump |
|
15 |
$419 |
3,218 |
11 |
Heat Pump |
|
16 |
$441 |
3,080 |
8 |
Heat Pump |
|
17 |
$522 |
2,507 |
20 |
Heat Pump |
|
18 |
$560 |
3,517 |
18 |
Heat Pump |
Predict the monthly heating bill for a house that has 2,600 square feet and has a heat pump that is nine years old.
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