To have the highest position within the class, the student would want a smaller standard deviation.
The student's inquiry about achieving the highest position within the class by manipulating the standard deviation involves understanding the dynamics of a normal distribution in statistics. In a normal distribution, the mean serves as the central point, and the standard deviation dictates the dispersion or spread of the scores around this mean.
A smaller standard deviation implies that the scores are more closely clustered around the mean, creating a narrower distribution. Conversely, a larger standard deviation indicates that the scores are more widely spread. In the context of the student's score of 75 on the statistics exam, desiring the highest position within the class would mean aiming for a situation where their score stands out relative to others.
Therefore, to achieve the highest position, the student would seek a scenario with a smaller standard deviation. This would result in a more concentrated cluster of scores around the mean, elevating the student's score of 75 in comparison. In essence, a smaller standard deviation would contribute to a more favorable positioning within the class distribution.