A courier company is trying to improve the quality of the services provided to its customers. For local deliveries, the company guarantees that all orders will be delivered within 24 hours. To justify the accuracy of their services, a preliminary study was conducted with a sample size of 200 deliveries. This showed that 186 deliveries were made within 24 hours.

a. Construct a 95% confidence interval for the true proportion of deliveries that are made within 24 hours.

b. Determine the additional samples that will be needed by the company if it wants to estimate the population proportion of deliveries that are made in 24 hours, within a margin of error of {0.02. and the same level of confidence as in part a.