Q4. Z Distribution: From Probabilities to Proportions (7 points)

Answer the following questions with this scenario:

In another initiative, the local school district would like to promote awareness of the students' BMI (body mass index) and encourage parents of students with extremely high or extremely low BMI to work with the school nurse in improving their children's health. The school district decides to measure all third-graders' BMIs, identify the highest 1% and the lowest 1% of the students, and then follow up with their parents. The graph below demonstrates the areas in the BMI distribution for the health program.

Helpful tips:

Review the tutorial videos on "how to use the Z table" before answering the following questions.

a. If we randomly draw one third-grader out of the school district, what is the probability of that child having a BMI that meets the criterion for the health program? (.5 point) Explain how you figure out the answer. (.5 point)

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 "significant" areas at the tails? (2 points total, 1 point for each critical Z) Explain how you find the answers. (1 point total, .5 point for each rationale)

c. If Lindsay's BMI is converted into a Z score of 2, is Lindsay included in the health follow-up program? (.5 point) Explain how you find the answer. (.5 point)

d. If the school district has a total of 400 third-graders, how many students' parents will be contacted by the school nurse? (Round the answer to a whole number) (1 point: .5 if the process is correct but the result was calculated incorrectly)

e. If the school district chooses a different strategy and sets the higher and lower cut-off points at Z values of +3 and -3, will the school nurse have more students or fewer students to follow up with, compared to the original cut-offs (1% at the upper and lower ends of the distribution)? (.5 point) Explain how you determined the answer. (.5 point)

\f