R2.10 Grading managers Many companies "grade on a bell curve" to compare the performance of their managers and professional workers. This forces the use of some low-performance ratings, so that not all workers are listed as "above average." Ford Motor Company's "performance management process" for a time assigned A grades, B grades, and C grades to the company's managers. Suppose that Ford's performance scores really are Normally distributed. This year, managers with scores less than received C's, and those with scores above received A's. What are the mean and standard deviation of the scores? Show your work.
Standard deviation: points
Ford Motor Company's "performance management process" for a time assigned,
No. of managers
Assuming: the performance scores are normally distributed.
Normal distributions are symmetric about the mean, so the mean must lie between the lowest and highest boundaries.
The mean essentially equals the average between these two boundaries:
Determine the z-score corresponding with (or 0.10) in table A:
As such, the lowest boundary lies localid="1649407327981" standard deviations below the mean.
As a consequence, the difference between the mean and the boundaries is 1.28 standard deviations:
Divide each side by
Each year, about million college-bound high school juniors take the PSAT. In a recent year, the mean score on the Critical Reading test was and the standard deviation was. Nationally, of test takers earned a score of 65 or higher on the Critical Reading test’s to scale.9
PSAT scores Scott was one of junior boys to take the PSAT at his school. He scored on the Critical Reading test. This placed Scott at the 68th percentile within the group of boys. Looking at all boys’ Critical Reading scores, the mean was and the standard deviation was
(a) Write a sentence or two comparing Scott’s percentile among the national group of test-takers and among the boys at his school.
(b) Calculate and compare Scott’s z-score among these same two groups of test-takers.
T2.5. The average yearly snowfall in Chillyville is Normally distributed with a mean of inches. If the snowfall in Chillyville exceeds inches in of the years, what is the standard deviation?
(a) inches(d) inches(b) inches(c) The standard deviation(c) inches cannot be computed from the given information.
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