Question: how to calculate 95 confidence interval by hand?
Answer: Because you want a 95% confidence interval, your z*-value is 1.96.
Suppose you take a random sample of 100 fingerlings and determine that the average length is 7.5 inches; assume the population standard deviation is 2.3 inches. ... 
Multiply 1.96 times 2.3 divided by the square root of 100 (which is 10).