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Answer :
Final answer:
The percentages of GMAT scores that are specified can be calculated using the z-score formula and the standard normal distribution table.
Explanation:
To find the percentage of GMAT scores that are 571 or higher, we need to calculate the standardized z-score. The z-score formula is given by: z = (x - mean) / standard deviation. Plugging in the values, we have z = (571 - 521) / 50 = 1. Using a standard normal distribution table, we can find that the percentage of scores that are 1 standard deviation above the mean is approximately 34.1%. Therefore, the percentage of GMAT scores that are 571 or higher is approximately 34.1%.
To find the percentage of GMAT scores that are 621 or higher, we again calculate the z-score: z = (621 - 521) / 50 = 2. Using the standard normal distribution table, we find that the percentage of scores that are 2 standard deviations above the mean is approximately 47.7%. Therefore, the percentage of GMAT scores that are 621 or higher is approximately 47.7%.
To find the percentage of GMAT scores that are between 471 and 521, we calculate the z-scores for both values: z1 = (471 - 521) / 50 = -1 and z2 = (521 - 521) / 50 = 0. We can then use the standard normal distribution table to find the area between these two z-scores, which is approximately 34.1% (the same as part a). Therefore, the percentage of GMAT scores that are between 471 and 521 is approximately 34.1%.
To find the percentage of GMAT scores that are between 421 and 571, we calculate the z-scores for both values: z1 = (421 - 521) / 50 = -2 and z2 = (571 - 521) / 50 = 1. Using the standard normal distribution table, we find that the area between these two z-scores is approximately 81.8%. Therefore, the percentage of GMAT scores that are between 421 and 571 is approximately 81.8%.
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