From a large population of married couples, researchers selected a random sample of four hundred couples.

The heights of the married men are approximately normally distributed, with a mean of 70 inches and a standard deviation of 3.

The heights of the married women are approximately normally distributed, with a mean of 65 inches and a standard deviation of 2.5.

There were twenty couples in which the wife was taller than her husband; in the other 380 couples, the husband was taller than his wife.

Find a 95% confidence interval for the proportion of the population for which the wife is taller than her husband.