Police station A investigates 26 cases over one month. In 11 cases, prosecutions are launched.

a. Construct the bootstrap distribution of the number of investigations where prosecutions are launched, using N = 10000 resamplings. Graphically display your results using a histogram or a bar plot.

b. Estimate (1 ) = 0.90 percentile confidence limits for the probability of an investigation results in a prosecution using a nonparametric bootstrap. As you may not be able to give an exact 90 % confidence interval, indicate the confidence limits of the interval you provide.

c. You are later told that on average, police launch prosecutions on 58 % of investigations undertaken. Based on the results in b, do you think there is something unusual about the prosecution policy of Police Station A.