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The Graduate Management Admission Test (GMAT) is a standardized test used for admission into various graduate management programs, such as MBA or Master of Finance. Suppose the GMAT scores of applicants for the Stanford MBA program are normally distributed with a mean of 651 and a standard deviation of 80. If Stanford decides to admit 30 percent of all applicants based on GMAT score ranking, what minimum GMAT score should be required for admittance?

Answer :

To determine the minimum GMAT score required for admittance to Stanford's MBA program, we need to find the score that separates the top 30% of applicants from the rest. This involves using the properties of the normal distribution.

Steps to Solve the Problem:

  1. Understand the Mean and Standard Deviation:

    • The mean (average) GMAT score is given as [tex]\mu = 651[/tex].
    • The standard deviation is given as [tex]\sigma = 80[/tex].

  2. Determine the Desired Percentile:

    • Stanford wants to admit the top 30% of applicants in terms of GMAT scores.
    • To find this, we need the GMAT score that corresponds to the 70th percentile of the distribution (100% - 30% = 70%) because percentiles indicate the percentage of scores below a certain point.

  3. Use the Z-Score Table:

    • A Z-score is a measurement of how many standard deviations an element is from the mean.
    • The Z-score corresponding to the 70th percentile can be found in a Z-score table. Typically, the Z-score for the 70th percentile is approximately 0.524.

  4. Calculate the Corresponding GMAT Score:

    • We use the Z-score formula:
      [tex]Z = \frac{X - \mu}{\sigma}[/tex]
    • Rearrange it to solve for [tex]X[/tex]:
      [tex]X = Z \cdot \sigma + \mu[/tex]
    • Substitute the known values:
      [tex]X = 0.524 \cdot 80 + 651[/tex]
      [tex]X = 41.92 + 651[/tex]
      [tex]X \approx 692.92[/tex]

  5. Conclusion:

    • Therefore, the minimum GMAT score required for admittance to be in the top 30% is approximately [tex]693[/tex].

This approach assumes the normal distribution of scores and that we are looking for the cutoff score above which 30% of the scores lie.

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