Handi Inc., a maker of cellphones, procures a standard display from LCD Inc. via an options contract.
At the start of quarter 1 (Q₁) Handi pays LCD $3.5 per option. At that time Handi’s forecast of demand in Q₂ is
Normally distributed with mean 24000 and standard deviation 6000. At the start of Q₂ Handi learns exact demand
for Q₂ and then exercises options at a fee of $4.5 per option (for every exercised option LCD delivers one display
to Handi). Assume Handi starts Q₂ with no display inventory and displays owned at the end of Q₂ are worthless.
Should Handi’s demand in Q₂ be larger than the number of options held, Handi purchases additional displays on
the spot market at $12 per unit.
For example, suppose Handi purchases 30000 options at the start of Q₁ but at the start of Q₂ Handi realizes that
demand is 35000 units. Then Handi exercises all of its options and purchases 5000 additional units on the spot
market. If, on the other hand, Handi realized demand is 27000 units, then Handi only exercises 27000 options.

If Handi chooses to purchase 28,000 options, what is the probability that Handi needs to purchase displays from the spot market?