Imagine that you were hired as a consultant for Arizona State University. ASU has provided you with data from the National Center for Education Statistics for four-year universities for the 2016-2017 academic year. Summary statistics for four indicators are provided below. Assume each indicator is normally distributed. Answer all of the questions for each of the four indicators. Show your work and make sure your final answers are easy to identify. You can round your answers to two digits after the decimal point.

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Part I: Calculating Z Scores and Using the Standard Normal Table
Imagine that you were hired as a consultant for Arizona State University. ASU has
provided you with data from the National Center for Education Statistics for four-year
universities for the 2016-2017 academic year. Summary statistics for four indicators are
provided below. Assume each indicator is normally distributed. Answer all of the
questions for each of the four indicators. Show your work and make sure your final
answers are easy to identify. You can round your answers to two digits after the decimal
point.
Indicator 1: SAT Math score for students admitted in 2016 who scored in the in the 75h
percentile (variable name: SATmath75th).
ASU West's score: 580
• University of Arizona's score: 790
Variable
Obs
Mean
Std. Dev.
Min
Max
SATmath75th
1,223
584.27
74.90
380.00
800.00
1. Identify the Z score that corresponds to ASU West's score
Answer:
2. Identify the percentage of universities with scores below ASU West's score
Answer:
3. Suppose ASU West would like to be in the same percentile as the University of
Arizona. What percentile would that be?
Answer:
4. Suppose ASU West would like to be in the top 10% of universities for this
indicator. What score would ASU West need to have?
Answer:
Transcribed Image Text:Part I: Calculating Z Scores and Using the Standard Normal Table Imagine that you were hired as a consultant for Arizona State University. ASU has provided you with data from the National Center for Education Statistics for four-year universities for the 2016-2017 academic year. Summary statistics for four indicators are provided below. Assume each indicator is normally distributed. Answer all of the questions for each of the four indicators. Show your work and make sure your final answers are easy to identify. You can round your answers to two digits after the decimal point. Indicator 1: SAT Math score for students admitted in 2016 who scored in the in the 75h percentile (variable name: SATmath75th). ASU West's score: 580 • University of Arizona's score: 790 Variable Obs Mean Std. Dev. Min Max SATmath75th 1,223 584.27 74.90 380.00 800.00 1. Identify the Z score that corresponds to ASU West's score Answer: 2. Identify the percentage of universities with scores below ASU West's score Answer: 3. Suppose ASU West would like to be in the same percentile as the University of Arizona. What percentile would that be? Answer: 4. Suppose ASU West would like to be in the top 10% of universities for this indicator. What score would ASU West need to have? Answer:
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