The accompanying data were compiled by the admissions office of a certain college during the past 5 years. The data relate the number of college brochures and follow-up letters (x) sent to a preselected list of high school juniors who took the PSAT and the number of completed applications (y) received from these students (both measured in thousands). Brochures Sent, x 1.1 2 3.8 5 6.2 Applications Completed, y 0.3 0.5 1 1.25 1.6 (a) Derive an equation of the straight line that passes through the points (2, 0.5) and (5, 1.25).y = (b) Use this equation to predict the number of completed applications that might be expected if 8000 brochures and follow-up letters are sent out during the next year. applications
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 accompanying data were compiled by the admissions office of a certain college during the past 5 years. The data relate the number of college brochures and follow-up letters (x) sent to a preselected list of high school juniors who took the PSAT and the number of completed applications (y) received from these students (both measured in thousands).
| Brochures Sent, x | 1.1 | 2 | 3.8 | 5 | 6.2 |
|---|---|---|---|---|---|
| Applications Completed, y | 0.3 | 0.5 | 1 | 1.25 | 1.6 |
y =
(b) Use this equation to predict the number of completed applications that might be expected if 8000 brochures and follow-up letters are sent out during the next year.
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