(a)on a normal distribution of exam scored, poindexter scored at the 10th percentile, so he claims that he outperformed 90% of his class. Why is he correct or incorrect? Because Foofy's score is in a tail of the distribution, she claims she had one of the highest scores on the exam. Why is she correct or incorrect?

(A) Wrong. 10th percentile means the lowest 10% of the class

(B) Neither right nor wrong. It depends on which tail end the scores fall upon

10th percentile means you scored equal to or better than 10% os the scores. 90% scored better than Foofy. She is in the wrong tail.

(a) Poindexter is incorrect in claiming that he outperformed 90% of his class. The 10th percentile represents the score below which 10% of the class falls. This means that 90% of the class outperformed Poindexter, as they scored above the 10th percentile.

Foofy is also incorrect in claiming that she had one of the highest scores on the exam. The tails of a normal distribution represent extreme scores, either very high or very low. So, being in the tail does not necessarily mean having one of the highest scores. The highest scores would be closer to the mean or located in the middle of the distribution.

To determine whether Poindexter and Foofy are correct in their claims, we need to understand how percentiles work and their relationship to the normal distribution of exam scores.

(a) Poindexter's claim:
Poindexter claims that he outperformed 90% of his class because he scored at the 10th percentile. However, his claim is incorrect. The percentile of a score represents the percentage of scores in a distribution that fall below that score. So, scoring at the 10th percentile means that 10% of the scores are below his score, while 90% of the scores are above his score. Therefore, Poindexter actually performed worse than 90% of his class.

To explain how to calculate this, we need to know the mean and standard deviation of the exam scores. Suppose the mean is represented by μ and the standard deviation by σ. We can use a standard normal distribution table or statistical software to find the z-score corresponding to the 10th percentile. The z-score represents the number of standard deviations a data point is from the mean.

Using the z-score, we can calculate Poindexter's score:
Score = μ + (z-score) * σ

(b) Foofy's claim:
Foofy claims that she had one of the highest scores on the exam because her score is in the tail of the distribution. Her claim depends on the specific context of what is considered a "high" score. If the exam scores follow a normal distribution, then extreme scores in the tails may indeed be considered high.

However, it's important to note that without further information about the distribution and the position of her score in relation to the mean and standard deviation, we cannot definitively determine whether Foofy's claim is correct or incorrect. To make a more precise determination, we would need to know the z-score of Foofy's score and compare it to the z-scores of other scores in the dataset.

In summary, Poindexter's claim is incorrect because scoring at the 10th percentile means he performed worse than 90% of his class. Foofy's claim cannot be definitively evaluated without more information about the distribution and other scores on the exam.