3. Concrete is delivered to a construction site 8 times each day, 5 days a week (Monday through Friday). As part of the quality control, the water-to-cement ratio, R, of each batch of concrete is measured. The water-cement ratio is known to be lognormally distributed with mean [1,; = 0.35 and coefcient of variation 6;; = 0.13. If the measured water-to-cement ratio of a batch is below 0.25 or greater than 0.45, then the concrete is rejected. Assume that the water-to-cement ratio of a batch of concrete is independent of the water-tocement ratio of any other batch. Also, when a batch of concrete is rejected, it is not replaced. a) [5 pts] What is the probability that a single batch of concrete is rejected? b) [5 pts] What is the expected (mean) number of batches of concrete that are rejected in one work week (5 days)? c) [10 pts] What is the probability that at least two batches of concrete are rejected in a 5- day work week? (1) [10 pts] What is the probability that the rst rejected batch of concrete of a week (Monday through Friday) is delivered on Tuesday