Question: We would like to know the percentage of new mobile operator customers in Banská Bystrica. We obtained the following results by public opinion survey. There were 35 customers of the new operator from 100 randomly selected respondents.

a) Find a 95% confidence interval for the population proportion of new mobile customers!

b) Find the maximal population proportion of new mobile operator customers with 95% confidence!

c) Find the minimal population proportion of new mobile operator customers with 90% confidence!

d) Assume that the maximum tolerable error \(\Delta \) has to be < 0.01. What number of respondents do we need?