-All numerical answers should be accurate to two decimal places -All numerical answers should be accurate to two decimal places (nearest hundredth); however, probabilities should be reported to four decimal places, if applicable. Do not forget units where applicable.A large dairy farm reports that the mean weight of their eight-month-old heifers is normally distributed with ?? = 475 lbs and ?? = 25 lbs. Define X = weight of an eight-month-old heifer. a) If you randomly select one heifer from this group, what is the probability that the heifer weighs less than 445 pounds? b) What weight separates the heaviest 6% of heifers from all heifers on the given dairy farm? c) A randomly selected heifer from this group weighs 485 pounds. What percentile does this correspond to?d) A random sample of 35 heifers is selected. What is the probability that the mean weight exceeds 477 pounds?MathStatistics and Probability STAT 311
