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 75m 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:

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 75m 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:

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Description: Part I: Calculating Z Scores and Using the Standard Normal TableImagine that you were hired as a consultant for Arizona State University. ASU hasprovided you with data from the National Center for Education Statistics for four-yearuniversities for t

MATLAB: An Introduction with Applications

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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

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Question

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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