I am having difficulty in solving the following type of questions and cannot understand the solution posted. Could you please explain the solution for the following questions?

400.2. Peter the Analyst has generated 800 independent scenarios of future single-period portfolio values. He observes the mean (average) of his simulated output distribution and determines a 95.0% confidence interval with a length of approximately $300.00; i.e., length is the difference between the upper and lower bound of the confidence interval. Peter's manager wants him to increase the accuracy of his estimate of the population's mean by reducing the length of the confidence interval to about $60.00. How many scenarios should Peter run?

a. 800; no change in trials but increase the confidence level

b. 4,000

c. 7,200

d. 20,000

P1. T2. Panchamanova.

4.

A Monte Carlo simulation consisting of 100 replications returns a 95% VaR quantile of 1.645 (as expected) with a standard error of 0.40, such that the confidence interval for the VaR quantile is [1.245,2.045]. This standard error is deemed too high. How many replications are approximately required in order to reduce the confidence interval to [1.545, 1.745]?

a) 200

b) 400

c) 800

d) 1,600