In a random sample of 75 individuals, 52 people said they prefer coffee to tea. 99.7% of the population mean is between what two values?

Sample size, n = 75
Point estimate, p = 52/75 = 0.693
Z at 99.7% confidence interval ≈ 2.96

Population mean interval = p+/- Z*Sqrt [p(1-p)/n]

Substituting;
Population mean interval = 0.693 +/- 2.96*Sqrt [0.693(1-0.693)/75] = 0.693+/-0.158 = (0.535,0.851) or (53.5%,85.1%)