3. (30 pts) Each clamp produced by a machine is OK with probability P, and faulty with probability 1 - P, independent of all else. Unfortunately, P depends on things such as maintenance etc that we cannot know for sure, so that it is reasonable to model P as a random variable that is uniformly distributed on (0.5, 0.75). The machine produces a single batch of 5 clamps each day, so it seems reasonable to assume that each clamp in a single batch sees the same value of P, but different batches see different values of P (a) Use simulation to compute the expected number of OK clamps in a batch of 5 clamps (call this g, say) HINT: The code in question 1 may be useful.] Give a 95% confidence interval for g that is accurate to approximately 1 decimal place, choosing the runlength appropriately (b) Use your simulation to give a 95% confidence interval for the probability, q say, that 4 or more of the 5 clamps in a batch are OK. You should choose the runlength so that your estimate of q is accurate to approximately 10% of the true value