D Question 9 11 pts A grocery supplier has two potato fields, A and B, growing the same kind of potato. However the field A produces potato with proportion of 0=5% of potatoes that are rotten inside, while field B produces 0=9% of rotten potatoes. The grocery manager asked the supplier to deliver potato from field A. The delivery arrived. The manager is bayesian and based on her prior experience with the supplier, she believes that the probability of the delivery being from field A (i.e. that the supplier is honest) is 40%. While the supplier hasn't left yet, the manager quickly checks 15 potatoes and discovers a = 2 of them to be rotten inside. Find the posterior probability P(0 = 0.05 | a = 2) that the potato comes from the field A, after finding 2 rotten potatoes in the sample. Round your answer to 3 decimal places. O 0.662 O 0.135 O 0.054 0.265 O 0.285D Question 3 11 pts A sample of 12 fossil skeletons of an extinct species of bird has been collected. The mean length of the skulls in this sample is 5.29 cm and the standard deviation of the sample is 0.21 cm. Assuming that such measurements are normally distributed, find a 95% confidence interval for the population mean length of the skulls of this species of bird You may want to use one of these at(p-0.025, af-11, lower.tail-FALSE) =2.200985 at (p.0.es, droll. lower. tail-FALSE) -1.795885 ahome(0. 825, mean-0. so-1, lower. tail-FALSE) -1.959964 gnomece.85, mean-@, sd-1, tower. tail-FALSE) =1.644854 (4.913,5.667) (5.181, 5.399) (5.171, 5.409) O (5.157, 5.423)D Question 4 11 pts Assume that prior distribution of probability of success 0 in a single Bernoulli trial has density 9(0) = 10 40 ,0