(a) Show that the data are linear. The difference in pounds of ice from 12:00 P.M. to 1:00 P.M. is , the difference from 1:00 P.M. to 2:00 P.M. is and the difference from 2:00 P.M. to 3:00 P.M. is . Because these values are all ---Select--- different the same , the function is linear. (b) Let t denote the time in hours since noon, and let I denote the pounds of ice made. Find a linear model for I as a function of t. I = (c) If 675 pounds of ice will be needed for the game tonight, will the ice machine produce enough ice by game time? YesNo
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.
Our ice machine is making ice in preparation for the game that starts at 7:00 P.M. The machine is monitored, and the amount of ice is recorded at the end of each hour. The results are in the table below.
| Time | 12:00 P.M. | 1:00 P.M. | 2:00 P.M. | 3:00 P.M. |
|---|---|---|---|---|
| Pounds of ice |
200 | 264 | 328 | 392 |
(b) Let t denote the time in hours since noon, and let I denote the pounds of ice made. Find a linear model for I as a function of t.
(c) If 675 pounds of ice will be needed for the game tonight, will the ice machine produce enough ice by game time?
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