In 1996, the Small Business Administration (SBA) granted 771 government-guaranteed loans to small businesses in North Carolina (The Wall Street Journal Almanac, 1998). Suppose a sample of 50 small businesses showed an average loan of $149,670 with a standard deviation of $73,420 and that 18 of the businesses in the sample were manufacturing companies.

a. Develop an approximate 95% confidence interval for the population mean value of a loan.

b. Develop an approximate 95% confidence interval for the total value of all 771 SBA loans in North Carolina.

c. In the sample, 18 of the 50 businesses were involved in manufacturing. Develop an approximate 95% confidence interval for the proportion of loans involving manufacturing companies.