The minimum scores are:
a) 674 is the minimum score necessary to receive $500
b) 306 is the minimum score to stay out of summer school
How to find the z-score?
a) 1 - 0.04 = 0.96, a z-score of 1.75 corresponds to 0.96 probability
1.75 = (X - 490)/105
X - 490 = 1.75 * 105
X = 183.75
X = 183.75 + 490
X = 673.75
674 is the minimum score necessary to receive $500
b) A z-score of -1.75 corresponds to 0.04 probability
-1.75 = (X - 490) / 105
X - 490 = -1.75 * 105
X = -183.75
X = -183.75 + 490
X = 306.25
306 is the minimum score to stay out of summer school