In the ambulance response time example (Exercise 8), a \(95 \%\) confidence interval with a width of approximately \(31 / 4\) minutes was constructed based on a sample of 67 runs \((N=67)\). Using the standard deviation of 6.64 as the estimate of the population standard deviation \((\hat{\sigma}) \ldots\)

a. How large should the sample be for a desired \(95 \%\) confidence interval width of 2 minutes?

b. How large should the sample be for a desired \(95 \%\) confidence interval width of 1 minute?

c. How large should the sample be for a desired \(95 \%\) confidence interval width of \(1 / 2\) minute ( 30 seconds)?