5. Suppose that the mean and standard deviation of the scores in a Statistics exam are 75 and 9.5 respectively.
   What minimum score should a student obtain to be a part of the top ? Round answers to 2 decimal places.
   93.62
   56.38

To determine the minimum score needed to be in the top 2.5%, we can use the concept of z-scores. A z-score represents how many standard deviations an element is from the mean. For the top 2.5%, the z-score is approximately 1.96 (since we’re looking at the upper tail of the normal distribution).

Using the formula , we can calculate the score:
, which rounds to 93.62.

Achieving this score means that a student would outperform 97.5% of their peers, making them standout scholars in the world of statistics!

Now, let’s take a moment to appreciate how standard deviations and means come to life in the classroom. Imagine everyone in class has different strengths and weaknesses, but this bell curve helps us understand how grades are distributed in an exam. It’s not just numbers; it’s a way to measure success, effort, and, yes, maybe a little bit of caffeine-fueled late-night study sessions!