A web based software company is interested in estimating the proportion of individuals who use the Firefox browser. In a sample of 200 of individuals, 19 users stated that they used Firefox. Using this data, construct a 99% confidence interval for the proportion of all individuals that use Firefox.
a) What is the lower limit on the 99% confidence interval? Give your answer to three decimal places.
b) What is the upper limit on the 99% confidence interval? Give your answer to three decimal places.
c) If you hadn't already taken the sample listed above, what sample size would be required so that the width of the 99% confidence interval would be at most 0.03 units wide? Be as conservative as possible with your answer!