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 example, assigns 10% A grades, 80% B grades, and 10% C grades to the company's 18,000 managers. suppose that Ford's performance scores really are normally distributed. this year, managers with scores less that 25 received C's and those with scores above 475 received A's. what are the mean and standard deviation of the scores?

I don't want the answer, just the steps.

From the Z table, the 10% tail is 1.282 std from the mean.

Since the 10% tail is used on both ends, the mean is halfway between where the tails start.

That help?

To find the mean and standard deviation of the scores, you will need to use the information provided about the grading percentages and thresholds. Here are the steps to calculate them:

1. Identify the cutoff scores for each grade:
- Cutoff score for C grade: Less than 25
- Cutoff score for A grade: Above 475

2. Calculate the z-scores for the cutoff scores:
- The z-score formula is given by: z = (x - μ) / σ
- For C grade cutoff score: z = (25 - μ) / σ
- For A grade cutoff score: z = (475 - μ) / σ

3. Determine the z-scores corresponding to the grading percentages:
- C grades: 10% or 0.10 (equivalent to cumulative probability 0.10)
- A grades: 10% or 0.10 (equivalent to cumulative probability 0.90)

4. Use a standard normal table or z-score calculator to find the z-scores:
- For C grade: Find the z-score that corresponds to a cumulative probability of 0.10. This will give you the z-score for the C grade cutoff.
- For A grade: Find the z-score that corresponds to a cumulative probability of 0.90. This will give you the z-score for the A grade cutoff.

5. Set up a system of equations using the z-scores and solve for the mean and standard deviation:
- Equation for C grade cutoff: z = (25 - μ) / σ
- Equation for A grade cutoff: z = (475 - μ) / σ
- Substitute the respective z-scores into these equations.

6. Solve the system of equations to find the mean (μ) and standard deviation (σ) of the scores.

Note: This process assumes that the scores are normally distributed, as stated in the problem.