Suppose Professor Alpha and Professor Omega teach finance. Records obtained from

past students indicate that students in Professor Alpha’s class have a mean score of 80%
with a standard deviation of 5%, while past students in Professor Omega’s class have a
mean score of 80% with a standard deviation of 10%. Decide which professor to take the
class from, using a statistical argument.

hard to say.

You have a better chance of scoring a nice safe 80% in Alpha's class
But you have a better chance of scoring higher in Omega's class. Of course, there's always a chance of scoring lower, as well.

Best bet -- study hard, and the teacher makes little difference.

To decide which professor to take the class from, we can compare the two professors based on the mean score and the standard deviation of their students' scores. The statistical argument will involve comparing these two measures.

First, let's understand what the mean score and standard deviation represent. The mean score is the average score of the students in each class, which gives an indication of the overall performance. The standard deviation measures the spread or variability of the scores around the mean, which gives an indication of how much the individual scores deviate from the average.

For Professor Alpha's class:
Mean score = 80%
Standard deviation = 5%

For Professor Omega's class:
Mean score = 80%
Standard deviation = 10%

To make a statistical comparison, we need to consider both the mean score and the standard deviation together. One way to do this is by using a Z-score.

The Z-score is a measure that indicates how many standard deviations away a particular score is from the mean. We can calculate the Z-scores for both classes using the formula:

Z = (X - μ) / σ

Where:
Z is the Z-score
X is the actual score
μ is the mean score
σ is the standard deviation

For Professor Alpha's class:
Z = (X - 80%) / 5%

For Professor Omega's class:
Z = (X - 80%) / 10%

Now, let's consider a hypothetical scenario where a student scores 85% in each class. We can calculate the Z-score for this score in both classes.

For Professor Alpha's class:
Z = (85% - 80%) / 5% = 1

For Professor Omega's class:
Z = (85% - 80%) / 10% = 0.5

The Z-score indicates how many standard deviations away the score is from the mean. A higher absolute value of the Z-score suggests that the score is relatively better compared to the other scores in the class.

In this scenario, the Z-score for Professor Alpha's class is 1, while the Z-score for Professor Omega's class is 0.5. This suggests that scoring 85% in Professor Alpha's class is relatively better compared to scoring the same in Professor Omega's class.

To generalize this comparison, we can say that because Professor Alpha's class has a smaller standard deviation (5%) compared to Professor Omega's class (10%), the individual scores in Professor Alpha's class tend to deviate less from the mean. This means that a given score is relatively better in Professor Alpha's class compared to Professor Omega's class.

Therefore, statistically speaking, based on the lower standard deviation and the Z-score comparison, it seems more advantageous to take the class with Professor Alpha. However, it is important to consider other factors such as teaching style, course materials, and personal preferences before making a final decision.