The germination rate of a particular seed is the percentage of seeds in the batch which successfully emerge as plants. Assume that the germination rate for a batch of sunflower seeds is 80%, and that among a large population of n seeds the number of successful germinations is normally distributed with mean μ = 0.8n and σ = 0.4√n.

a. In a batch of n = 2500 seeds, what is the probability that at least 1960 will successfully germinate?

b. In a batch of n = 2500 seeds, what is the probability that at most 1980 will successfully germinate?

c. In a batch of n = 2500 seeds, what is the probability that between 1940 and 2020 will successfully germinate?