School A wanted to establish a new gifted math program for sixth graders so they administered a standardized math aptitude test to all sixth graders. The school determined that students scoring in the top 5% would be considered exceptional in math abilities so they would be included in the gifted program. The graph below illustrates the area of the Z distribution where students' performance would be considered "significantly better" than the general sixth-grader population.

a) What is the probability of randomly drawing one of those exceptional students from the whole pool of sixth graders in the school?

.05

b) If the school tested 500 students (this means that the whole distribution contains 500 student scores), how many would be identified as meeting this criterion of having exceptional math abilities (who scored significantly higher than the general sixth grade population)?

5% of gifted, .05 probability of drawing a gifted student, thus 5% would be identified as being gifted.

c) If your child, Katie, scored at 97th percentile on this test, would she be selected for the gifted program? Why or why not?

d) If we use a Z distribution to represent the students' test scores, what is the Z score that serves as the critical (or cutoff) value for this "significance" area of the distribution?

e) Out of all the sixth graders' test scores, the mean () was 100 and the standard deviation () was 15. Based on the critical Z score (from question d above) for the significance area of the distribution, what would be the minimum raw score required for entering the gifted program?

f) As mentioned before, Katie scored at the 97th percentile on this test. What was Katie's actual (raw) test score?