Question

The Empirical Rule is based on the standardized normal distribution.

1. Describe how you could use the Empirical Rule to evaluate the distribution of scores on a national test. You are given the following information for the national test: (1) the population mean = 450 and (2) the population SD = 75.
2. Second, based on the information given above, estimate the range of scores on this test. That is, estimate the low score and the high score on the test. Discuss how you arrived at your estimate for each score.
3. Finally, determine where students’ test scores on the national test would place them in terms of their percentile ranking. You are given the following information on test scores of three students.
   
   
4. Student A scored a 600. What percentile is this student?
5. Student B scored a 225. What percentile is this student?

Let’s say a student’s score placed them in the 99th percentile. Estimate the student’s score using whatever means gives you a good estimate.

Answer 1

a)We will have to standardize the test scores and then calculate the probability of the students above and below the scores.

b)As the scores are distributed normally, we can assume the scores to bottom out at -3 and +3 Standard deviations.

c)The above scores would place the students at 0.13 percentile and 99.87 percentile