Would you rather take an exam that typically has an mean of 80 with a standard deviation of 3 or an exam with a mean of 80 with a standard deviation of 15? why?
I would take the 80% with a standard deviation (σ) of 3%. This way, 68% of the time, I would get between 77% and 83%, and 95% of the time I get between 74% and 86%.
If you are a risk taker and take σ=15%, then there is a 9.12% that you'll get below 60%.
Check my calculations using a normal distribution table, or from the link below:
http://www.mathsisfun.com/data/standard-normal-distribution-table.html
Thank You
To determine whether it would be better to take an exam with a mean of 80 and a standard deviation of 3, or an exam with a mean of 80 and a standard deviation of 15, we need to understand what these statistics represent and their implications.
The mean represents the average value, in this case, the average score on the exam. The standard deviation measures the spread or dispersion of the scores around the mean. A smaller standard deviation indicates that the scores are closely clustered around the mean, while a larger standard deviation suggests that the scores are more spread out.
In this scenario, the first exam has a smaller standard deviation of 3. This means that the scores on this exam are closely clustered around the mean of 80, with most scores falling within a small range. On the other hand, the second exam has a larger standard deviation of 15, indicating that the scores are more widely spread out around the mean.
If you prefer a higher chance of getting a score close to the mean, with less variability in scores, then taking the exam with a mean of 80 and a standard deviation of 3 would be preferable. This indicates that most students' scores would be very close to the mean, making it easier to predict what you might score on the exam.
However, if you are comfortable with a wider range of potential scores and are willing to take more risks, then the exam with a mean of 80 and a larger standard deviation of 15 might be more suitable. Keep in mind that this higher variability also means that there is a greater chance of scoring significantly above or below the mean.
Ultimately, the decision depends on your personal preferences and risk tolerance. If you value consistency and predictability, the first exam might be a better choice. If you are comfortable with a wider range of potential outcomes and are willing to take more risks, the second exam might be more appealing.