50 MATH PROFESSORS WERE ASKED HOW LONG IT TAKES TO GRADE A STUDENT'S HOMEWORK ASSIGNMENT. THE MEAN GRADING TIME FOR THE SAMPLE WAS 36.2 MINUTES WITH A STANDARD DEVIATION OF 4.8 MINUTES. WHAT IS THE 99% CONFIDENCE INTERVAL FOR THE MEAN GRADING TIME OF ALL MATH PROFESSORS?

50 MATH PROFESSORS WERE ASKED HOW LONG IT TAKES TO GRADE A STUDENT'S HOMEWORK ASSIGNMENT. THE MEAN GRADING TIME FOR THE SAMPLE WAS36.2 MINUTES WITH A STANDARD DEVIATION OF 4.8 MINUTES. WHAT IS THE 82% CONFIDENCE INTERVAL FOR THE MEAN GRADING TIME OF ALL MATH PROFESSORS?

First, please do not use all capitals. Online it is like SHOUTING. Not only is it rude, but it is harder to understand. Thank you.

99% = mean ± 1.645 SD, .005 of scores are beyond at each end.

82% = mean ± 1.342 SD, .09 of scores are beyond at each end.

These values were found in a table table in the back of your statistics text labeled something like "areas under normal distribution."

To calculate the 99% confidence interval for the mean grading time of all math professors, you can use the formula:

Confidence Interval = Mean ± Critical Value * (Standard Deviation / sqrt(n))

where:
Mean = Sample mean
Critical Value = Z-Score corresponding to the desired confidence level (in this case, 99%)
Standard Deviation = Sample standard deviation
n = Sample size

In this case, the mean grading time for the sample is 36.2 minutes with a standard deviation of 4.8 minutes. The sample size is not provided in the question, so we'll assume it to be 50 (as stated in the question).

First, we need to find the Z-Score corresponding to a 99% confidence level. You can use a Z-Table or a statistical calculator to find the Z-Score. The Z-Score for a 99% confidence level is approximately 2.576.

Now we can calculate the confidence interval:

Confidence Interval = 36.2 ± 2.576 * (4.8 / sqrt(50))

Calculating the square root of 50, we get:

Confidence Interval = 36.2 ± 2.576 * (4.8 / 7.071)

Simplifying further, we get:

Confidence Interval = 36.2 ± 2.576 * 0.678

Finally, calculating the upper and lower bounds of the confidence interval:

Lower Bound = 36.2 - (2.576 * 0.678) ≈ 35.396
Upper Bound = 36.2 + (2.576 * 0.678) ≈ 37.004

Therefore, the 99% confidence interval for the mean grading time of all math professors is approximately 35.396 minutes to 37.004 minutes.