a) If we randomly draw one student
out of school district, what is probability of that child having a BMI that is either in the highest 5% or the lowest 5% of the distribution?
b) If the BMI distribution is converted into a Z distribution, what would be the upper critical Z value and the lower critical Z value that mark the two extremes?
c) If Charlotte's BMI is converted into a Z score of -1.35, what is the probability of drawing a student out of the school district that has a Z score that is equal or lower than Charlotte's Z score?
d) If the school district has a total of 20,000 students (which means the whole distribution contains 20,000 BMI scores), how many of them would have a BMI that is equal to or lower than Charlotte's BMI? (1 pt for formula/work, 1 pt for answer)
e) If the school district sets the higher and lower cut-off points at Z values of +1.75 and
-1.75, will the school nurse have more students or fewer students to follow up with, compared to the original cut-offs of 5% at either extreme of the distribution? (1 pt for answer, 1 pt for rationale/calculation)