Final answer:
Standardizing a positively skewed distribution of scores does not change the skewness; the distribution remains positively skewed after standardization.
Step-by-step explanation:
When you standardize a distribution of scores that are positively skewed, the distribution remains positively skewed. Standardization is a process where you convert original scores in a data set to z-scores, which are a measure of how many standard deviations an individual score is from the mean. However, this transformation does not alter the shape of the distribution.
When dealing with a positively skewed distribution, the mean is typically greater than the median. The tail of the distribution stretches out towards the right, or positive direction, hence the 'positive' skewness. The act of standardizing this positively skewed distribution results in a new set of scores that have a mean of 0 and a standard deviation of 1, but the shape of the distribution, including the direction of skewness, remains unchanged.
Even after standardization, if you graph the standardized scores, the tail will still stretch out to the right. It's important to remember that standardization only changes the scale of the scores and does not alter the underlying distribution's shape. Therefore, the correct answer to the student's question is (c) The standardized scores will also be positively skewed.