In a class of 30 students, the teacher records the scores of a test. The average score of the class is 78. After the test, the teacher discovers that one student was wrongly recorded as scoring 85 instead of 95. If the new average score is recalculated, what is the probability that a randomly selected student from this class scored above the new average? Assume the distribution of scores remains consistent with the initially provided information.

To find the new average, first calculate the total score before the correction:

$$ ext{Total Score} = ext{Average Score} imes ext{Number of Students} = 78 imes 30 = 2340 $$

Now adjust for the corrected score:

$$ ext{Corrected Total Score} = 2340 - 85 + 95 = 2350 $$

The new average score will be:

$$ ext{New Average} = rac{2350}{30} $$