The buffon's needle experiment was conducted and the results were that 4 out of the 15 needles dropped crossed the line on the floorboards. The value for d was 8cm and the value for L was 4cm. Thus the probability of the needle crossing the line is 4/15 and the estimation of pi=3.75. Given this data, complete the following tasks

a) 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 2l/(dpi), where the needle has length l and the floorboards are of width d > l. Perform a hypothesis test at the 0.05 significance level to determine whether your results are consistent with this prediction.
c) 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 pi correct to 2 decimal places?