Answer :
Final answer:
To find the minimum GMAT score needed to be admitted to the top MBA program, we calculate the z-score for the upper 4% of GMAT scores. The minimum score needed is 665 points.
Explanation:
To find the minimum GMAT score needed to be admitted to the top MBA program, we need to calculate the z-score for the upper 4% of the GMAT scores. The z-score represents the number of standard deviations a data point is from the mean.
The formula for calculating the z-score is: z = (x - μ) / σ, where x is the data point, μ is the mean, and σ is the standard deviation.
In this case, since we want to find the minimum score, we need to find the z-score that corresponds to the upper 4% level, which is the same as finding the z-score for the lower 96% level.
We can use a standard normal distribution table or a calculator to find the z-score that corresponds to a cumulative probability of 0.96. Once we have the z-score, we can solve for x using the formula: x = (z * σ) + μ.
Substituting the values given in the question, we have: x = (z * 125) + 550.
Rounding the answer to a whole number, the minimum GMAT score needed to be admitted to the top MBA program is 665 points.
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