36.1k views
0 votes
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 means that you:

A. have a score that is 1.5 times the average for the class.
B. are 1.5 standard deviations above average for the class.
C. are 1.5 points above average for the class.
D. have a standard deviation of 1.5.

1 Answer

2 votes

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.

User Bachor
by
8.6k points