Why can a subtraction problem be written as an addition problem without changing the outcome?
give a real-world scenario where this might be modeled

First let’s find the mean and standard deviation for both test and then we can calculate the probability of getting that score in his respective test and compare. 

First test

P(x < 56)

P(z < 56-47.80/16.38)

P(z<0.50) = 1 – 0.3085 = 0.6915 or 69 percentile

Second test

P(x < 74)

P(z < 74 – 73.45 / 8.37)

P(z<0.07) = 1 – 0.4721= 0.5279 or 53 percentile

The probability for this normal distribution also means the percentile, so we can say that in the first test she was in the 69 percentile while in the second test she was in the 53 percentile. Therefore, she did worse in the second test