Question 6 /10 Marks) Recall the Buffon's needle experiment from Question 6 of Assignment 1. Use your results from the experiment that you performed for that question, or generate new results, to perform the following tasks. Construct a 95% confidence interval for the probability a needle crosses a line. b) It can be shown that the exact probability of crossing a line is 2//(da), where the needle has length / and the floorboards are of width d > /. Perform a hypothesis test at the 0.05 significance level to determine whether your results are consistent with this prediction. Is the result of the hypothesis test in part b) consistent with the confidence interval constructed in part a)? Explain why or why not. d) What sample size would be needed to estimate or correct to 2 decimal places? You may have attempted this same question for Assignment 1, but this time answer it using the sample size calculation approach we have learned since then