Final answer:
A standardized score of +1.5 signifies that the score is 1.5 standard deviations above the class average according to a Normal model. It does not mean 1.5 times the average, just a relative measure indicating how far your score deviates from the mean. The correct answer is option D. have a standard deviation of 1.5.
Step-by-step explanation:
If Mr. Kurz has created a Normal model to describe student scores in Math 134 and then tells you that you have a standardized score of +1.5, this indicates that your score is 1.5 standard deviations above the average for the class. In this context, the standardized score refers to a z-score, which is a way of describing a score's relationship to the mean (average) in units of standard deviations. Choosing from the options given, the correct answer is B: you are 1.5 standard deviations above average for the class.
For example, assuming the mean score for the SAT math section is 520 with a standard deviation of 115, a z-score of 1.5 would mean a score of approximately 692.5, calculated as 520 + 1.5(115). This score of 692.5 is 1.5 standard deviations above the mean.
Similarly, with IQ tests, where the mean is often 100 and the standard deviation is 15, a z-score of +1 would correspond to an IQ of 115, which is one standard deviation above the average IQ score. This interpretation is consistent across different contexts.