Based upon historical data, the successful seed germination rate for a certain variety of lettuce is 31%. A plant nursery has recently sowed 10,000 of these seeds, and then shortly after received orders for lettuce plants that can only be filled from successful germinations from this sowing.
a) If the order is for 3,000 lettuce plants, what is the probability that they can fill all of these orders?
b) Redo Part (a) for an order of 3,300 lettuce plants.
c) Failing to deliver on orders is something that cannot be 100% avoided in this line of work. However, one can decide on a maximum acceptable level of risk of this failure occurring. If this particular nursery is willing to accept a risk of such failure - ie, of not having enough germinated plants from a sowing to meet all orders - of up to but not exceeding 5%, then what is the largest total amount of plants it should take orders for, for each sowing of 10,000 of these seeds?