A Federal Reserve Bank of Atlanta report looks at what strategies and measures financial institutions are pursuing to provide mobile financial services to their customers. In response to a survey question about barriers hindering greater consumer adoption of mobile banking, in a survey of 115 financial institutions, 81 said security concerns is a barrier, 68 said lack of trust in the technology is a barrier, and 16 said difficulty of use was a barrier.

Construct a 95% confidence interval estimate of the population proportion of financial institution who said:

a. security concerns are a barrier hindering greater consumer adoption of mobile banking.

b. lack of trust is a barrier hindering greater consumer adoption of mobile banking.

c. difficulty of use is a barrier hindering greater consumer adoption of mobile banking.

d. You have been asked to update the results of this study. Determine the sample size necessary to estimate, with 95% confidence, the population proportions in (a) through (c) to within ±0.02.