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Answer :
The Z-scores: Z1 = (426 - 525) / 50 = -1.98 and Z2 = (576 - 525) / 50 = 1.02. Using the Z-table or calculator, the percentage of scores between these two values is approximately 81.73%.
The GMAT scores are normally distributed with a mean of 525 and a standard deviation of 50. To calculate the percentage of scores for each given range, we need to use the Z-score formula. The Z-score measures the number of standard deviations a given value is from the mean.
a) To find the percentage of GMAT scores that are 576 or higher, we need to find the Z-score for 576 using the formula: Z = (x - μ) / σ. Substituting the values, we get Z = (576 - 525) / 50 = 1.02. Using a Z-table or calculator, we can find that the percentage of scores above 1.02 is approximately 15.89%.
b) Similarly, for scores of 626 or higher, we find the Z-score: Z = (626 - 525) / 50 = 2.02. Using the Z-table or calculator, the percentage of scores above 2.02 is approximately 2.22%.
c) To find the percentage of scores between 476 and 526, we need to find the Z-scores for both values. Z1 = (476 - 525) / 50 = -0.98 and Z2 = (526 - 525) / 50 = 0.02. By looking up the Z-scores on the Z-table or using a calculator, we find the percentage of scores between these two values is approximately 34.27%.
d) To find the percentage of scores between 426 and 576, we calculate the Z-scores: Z1 = (426 - 525) / 50 = -1.98 and Z2 = (576 - 525) / 50 = 1.02. Using the Z-table or calculator, the percentage of scores between these two values is approximately 81.73%.
In summary:
a) The percentage of GMAT scores that are 576 or higher is approximately 15.89%.
b) The percentage of GMAT scores that are 626 or higher is approximately 2.22%.
c) The percentage of GMAT scores between 476 and 526 is approximately 34.27%.
d) The percentage of GMAT scores between 426 and 576 is approximately 81.73%.
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