It is said that the salaries of all associate professors in a particular region follow a normal distribution with a mean of $224,500 and a standard deviation of $62.37. To verify this statement, a random sample of 28 associate professors is taken from the same population. Assuming that their salaries are independent, what is the probability that the total salary of these associate professors falls between $6,281,070 and $6,289,510?

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