1. A random sample of 25 precocious readers is drawn and their family backgrounds carefully studied. In 40% of the cases, the child's father is at least 15 years older than the mother. Place a 90% confidence interval on the proportion of such age disparities between the parents of precocious readers.
2. A random sample of 100 persons suffering from mental depression reveals that 75 of them cannot properly evaluate their job skills.
a. Give the maximum-likelihood estimate of the binomial parameter.
b. Set up a 95% confidence interval for this parameter.