The U.S. Postal Service (USPS) has used optical character recognition (OCR) since the mid-1960s. In 1983, USPS began deploying the technology to major post offices throughout the country (www.britannica.com). Suppose that in a random sample of 500 handwritten zip code digits, 466 were read correctly. 

(a) Construct a 95% confidence interval for the true proportion of correct digits that can be automatically read.

(b) What sample sample size is needed to reduce the margin of error to 1%?

(c) How would the answer to part (b) change if you had to assume that the machine read only one-half of the digits correctly?