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?

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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?

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