A random sample of size 25 is taken from a normal population having a mean of 75 and a standard deviation of 6. A second random sample of size 81 is taken from a different normal population having a mean of 60 and a standard deviation of 3. Find the probability that the sample mean computed from the 25 measurements will exceed the sample mean computed from the 81 measurements by at least 12.7 but less than 16.1. Assume the difference of the means to be measured to the nearest tenth.

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