In a random sample of 150 customers of a high-speed internet provider, 63 said that their service had been interrupted one or more times in the past month.

a. Find a 95% confidence interval for the proportion of customers whose service was interrupted one or more times in the past month.

b. Find a 99% confidence interval for the proportion of customers whose service was interrupted one or more times in the past month.

c. Find the sample size needed for a 95% confidence interval to specify the proportion to within ± 0.05.

d. Find the sample size needed for a 99% confidence interval to specify the proportion to within ± 0.05.