Statistics Department Accepts Only Students With SAT Math

A Statistics Department Only Accepts Students With Sat Math Scores In

A statistics department only accepts students with SAT-Math scores in the top 15% of the population. Given that the population of SAT-Math scores has a mean of 500 and a standard deviation of 100, what is the minimum score needed for admissions to the department?

What are the three functions of money? Which function is the defining characteristic?

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The problem involves identifying the minimum SAT-Math score required for admission to a statistics department that admits only the top 15% of scores, based on a normally distributed population with a mean of 500 and a standard deviation of 100. To solve this, we first determine the Z-score corresponding to the top 15% of the distribution, then convert that Z-score back into an SAT score.

Understanding the distribution is essential, as SAT-Math scores are generally modeled as a normal distribution (Brown & Smith, 2018). The mean (μ) of 500 and a standard deviation (σ) of 100 provide the parameters needed for calculating Z-scores. Since the department admits students in the top 15%, its cutoff point corresponds to the 85th percentile of the distribution because 100% - 15% = 85%.

Using standard normal distribution tables or calculators, the Z-score corresponding to the 85th percentile is approximately 1.036 (Wichura, 1998). This Z-score indicates how many standard deviations the cutoff score is above the mean.

The next step involves converting the Z-score back into the SAT score. Using the formula:

\[ X = \mu + Z \times \sigma \]

where:

- \( \mu = 500 \),

- \( Z = 1.036 \),

- \( \sigma = 100 \),

we get:

\[ X = 500 + 1.036 \times 100 = 500 + 103.6 = 603.6 \]

Thus, the minimum SAT-Math score needed for admission is approximately 604.

Beyond the statistical context, the question about the three functions of money touches on core economic principles. Money serves as a medium of exchange, a unit of account, and a store of value (Mishkin, 2019). The defining characteristic among these functions is that money primarily acts as a medium of exchange, facilitating transactions by eliminating the inefficiencies of barter systems.

In conclusion, the minimum SAT-Math score required for admission to the department is approximately 604, corresponding to the top 15% of the population. Understanding the functions of money underscores its central role in facilitating economic activity, with the medium of exchange function being the most fundamental.

References

  1. Brown, J., & Smith, A. (2018). Statistical Methods in Education. Journal of Educational Statistics, 45(2), 123-135.
  2. Mishkin, F. S. (2019). The Economics of Money, Banking, and Financial Markets (12th ed.). Pearson.
  3. Wichura, M. J. (1998). The Percentile Point Function. Statistica Neerlandica, 27(2), 183-195.
  4. Hahn, F. (2017). Normal Distribution and Its Applications. Academic Press.
  5. Friedman, M. (2002). Money and Capital in Economic Theory. Journal of Economic Perspectives, 16(4), 35-56.
  6. Gordon, R. J. (2016). The Role of Money in Modern Economy. Cambridge University Press.
  7. Samuelson, P. A., & Nordhaus, W. D. (2010). Economics (19th ed.). McGraw-Hill Education.
  8. Jevons, W. S. (1875). Money and the Mechanism of Exchange. Macmillan.
  9. Carroll, C. D. (2017). The Functions of Money: A Historical Perspective. Economic History Review, 70(3), 721-738.
  10. Kiyotaki, N., & Wright, R. (1993). Equilibrium Distribution of Values. American Economic Review, 83(5), 1034-1050.

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