The more corn a farmer plants per acre, the greater is the yield the farmer can expect, but only up to a point. Too many plants per acre can cause overcrowding and decrease yields. The data give crop yields per acre for various densities of corn plantings, as found by researchers at a university test farm. Density (plants/acre) 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000 Crop yield (bushels/acre) 42 97 117 139 141 121 92 66 (a) Find the quadratic polynomial that best fits the data. (Let y be the crop yield in bushels/acre and x the density in thousands of plants/acre. Round all numerical values to three decimal places.) y = (b) Draw a graph of the polynomial from part (a) together with a scatter plot of the data. (c) Use your result from part (b) to estimate the yield for 39,000 plants per acre. (Round your answer to the nearest integer.) bushels/acre
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.
The more corn a farmer plants per acre, the greater is the yield the farmer can expect, but only up to a point. Too many plants per acre can cause overcrowding and decrease yields. The data give crop yields per acre for various densities of corn plantings, as found by researchers at a university test farm.
| Density (plants/acre) |
15,000 | 20,000 | 25,000 | 30,000 | 35,000 | 40,000 | 45,000 | 50,000 |
| Crop yield (bushels/acre) |
42 | 97 | 117 | 139 | 141 | 121 | 92 | 66 |
(b) Draw a graph of the polynomial from part (a) together with a
bushels/acre
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