Question

Q4. Z Distribution: From Probabilities to Proportions (percentages) (7 points) Answer the following questions with this scenario: A school district runs a gifted language program in fourth grade with a selection criterion of 97th percentile. That is, students who score at 97th percentile or above on a standardized language test are eligible for the gifted program. Answer the following question based on this scenario. Helpful tips: Review the tutorial videos on "how to use the Z table" before answering the following questions. 97% a. What is the probability of randomly drawing a student from the whole population of fourth-graders that would meet the selection criterion for the gifted program? (.5 point) Explain how you determined the answer. (.5 point) b. If the district has 334 fourth-graders in total, how many will be eligible for the gifted program? (1 point, deduct .5 if the process is correct but the result was calculated incorrectly) c. If we use a Z distribution to represent all the test scores from the fourth-graders, what is the Z score that serves as the critical (or cutoff) value for determining eligibility for the gifted program? (2 points, both the answer and the rationale must be correct to earn the credit.) d. This standardized test used for the screening process has a published raw score mean (?) of 67 and standard deviation (?) of 15. Based on the critical Z score (from question c above, what would be the critical test score if we use the original raw scores to determine the students' eligibility? (1 point, deduct .5 if the process is correct but the result was calculated incorrectly) e. Saylor has a raw score of 92, is she eligible for the gifted program? Explain your rationale for this answer. (1 point, both the answer and the rationale must be correct to earn the credit) f. Davis has a Z score of 1.97, is he eligible for the gifted program? Explain your rationale for this answer. (1 point, both the answer and the rationale must be correct to earn the credit)

Q4. Z Distribution: From Probabilities to Proportions (percentages) (7 points)
Answer the following questions with this scenario:
A school district runs a gifted language program in fourth grade with a selection criterion of 97th percentile. That is,
students who score at 97th percentile or above on a standardized language test are eligible for the gifted program.
Answer the following question based on this scenario.

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

97%

a. What is the probability of randomly drawing a student from the whole population of fourth-graders that would
meet the selection criterion for the gifted program? (.5 point) Explain how you determined the answer. (.5 point)

b. If the district has 334 fourth-graders in total, how many will be eligible for the gifted program? (1 point, deduct
.5 if the process is correct but the result was calculated incorrectly)

c. If we use a Z distribution to represent all the test scores from the fourth-graders, what is the Z score that serves
as the critical (or cutoff) value for determining eligibility for the gifted program? (2 points, both the answer and the
rationale must be correct to earn the credit.)

d. This standardized test used for the screening process has a published raw score mean (?) of 67 and standard
deviation (?) of 15. Based on the critical Z score (from question c above, what would be the critical test score if we
use the original raw scores to determine the students' eligibility? (1 point, deduct .5 if the process is correct but
the result was calculated incorrectly)

e. Saylor has a raw score of 92, is she eligible for the gifted program? Explain your rationale for this answer. (1
point, both the answer and the rationale must be correct to earn the credit)

f. Davis has a Z score of 1.97, is he eligible for the gifted program? Explain your rationale for this answer. (1 point,
both the answer and the rationale must be correct to earn the credit)

Q4. Z Distribution: From Probabilities to Proportions (percentages) (7 points)
Answer the following questions with this scenario:
A school district runs a gifted language program in fourth grade with a selection criterion of 97th percentile. That is,
students who score at 97th percentile or above on a standardized language test are eligible for the gifted program.
Answer the following question based on this scenario.

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

97%

a. What is the probability of randomly drawing a student from the whole population of fourth-graders that would
meet the selection criterion for the gifted program? (.5 point) Explain how you determined the answer. (.5 point)

b. If the district has 334 fourth-graders in total, how many will be eligible for the gifted program? (1 point, deduct
.5 if the process is correct but the result was calculated incorrectly)

c. If we use a Z distribution to represent all the test scores from the fourth-graders, what is the Z score that serves
as the critical (or cutoff) value for determining eligibility for the gifted program? (2 points, both the answer and the
rationale must be correct to earn the credit.)

d. This standardized test used for the screening process has a published raw score mean (?) of 67 and standard
deviation (?) of 15. Based on the critical Z score (from question c above, what would be the critical test score if we
use the original raw scores to determine the students' eligibility? (1 point, deduct .5 if the process is correct but
the result was calculated incorrectly)

e. Saylor has a raw score of 92, is she eligible for the gifted program? Explain your rationale for this answer. (1
point, both the answer and the rationale must be correct to earn the credit)

f. Davis has a Z score of 1.97, is he eligible for the gifted program? Explain your rationale for this answer. (1 point,
both the answer and the rationale must be correct to earn the credit)

Added by Heather N.

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