Stochastic dominance and normal distributions

The profits from sales of a product depend on demand, which follows a normal distribution. The demand in week 1 has a distribution with mean 1000 and standard deviation 100. The demand in week 2 has mean 1010.

(a) Suppose that the standard deviation of demand in week 2 is 100. Explain why the profit in week 2 stochastically dominates the profit in week 1, and this result does not depend on the exact relationship between profit and sales.

(b) Show that if demand in week 2 has the standard deviation of 105, then the profit in week 2 will not stochastically dominate the profit in week 1.

(c) Show that if demand in week 2 has the standard deviation of 95, then the profit in week 2 will not stochastically dominate the profit in week 1.