Supplementary Exercise 8.98 of IPS7e
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n=975 university students examined with respect to change of major during 
college years. X = number of those students that did change major. Observed 
X=411. Assume X to follow B(875,p). (An approximate binomial setting, because 
sampling is from a finite population, but meeting the requirement than N>20*n.)

(a) sample proportion: p_hat = X/n = 0.470,
    standard error of p_hat: sqrt(p_hat*(1-p_hat)/n) = 0.0169
    classical approximate 95% CI for p: 0.470 +- 1.96*0.0169 = (0.437,0.503)
The classical CI should be perfectly fine here with a large number of positives 
and negatives. 

(b) in percent: 95% CI is (43.7%,50.3%)

(c) in numbers for a population of 37,000:
                95% CI is 37,000*(0.437,0.503) = (16,155; 18,603),
                using all decimals in the calculation