For a population with p = 0.6, find the probability for each sample proportion and given sample size.

(a) n = 12 and p̂ < 0.77

(b) n = 30 and p̂ > 0.56

(c) n = 65 and 0.54 < p̂ < 0.56

(d) n = 100 and p̂ < 0.69

(e) n = 240 and p̂ > 0.53