You have a friend who likes to try and classify the cars that drive past their bedroom window, but you think that you can build a convolutional neural network that can do a better job than your friend. To test how well your CNN works you test it on 140 cars. Let Z, be equal to 1 if the ith car make and model is correctly classified and 0 otherwise, for i = 1,..., 140. (a) What is the statistic that you will use to estimate the accuracy of your CNN? How do you compute it using Z₁, Z2,..., Z140? (b) Assuming that the accuracy of your algorithm is 0.94, can we approximate the sampling distribution of the statistic that you selected in part (a) using a normal distribution? Please state and check the requirements for applying the approximation, and identify the mean and standard deviation of the normal distribution. (Round your standard deviation to 3 sig figs.) (c) Your friend correctly classifies 97% of cars that they see on average. What is the probability that your randomly drawn sample is such that your sample statistic from (a) is higher than 0.97? (Round to 3 sig figs.) (d) You CNN's performance would be indistinguishable from your friend's performance if the sample of 140 cars allows you to construct a symmetric 95% confidence interval that contains 0.97. Say your algorithm correctly classifies 126 cars. Is your CNN's performance indistinguishable from your friend's performance?