Part C: Normal Random Variables and Probability (8 marks) The scores of students in a standardized test follow a normal distribution with a mean () of 150 and a standard deviation () of 20 . Calculate the probability that a randomly selected student's score is in the top 15% of all scores. Show your calculations. A factory produces light bulbs, and their lifetimes follow a normal distribution with a mean of 1,200 hours and a standard deviation of 100 hours. Calculate the probability that a randomly selected light bulb will last between 1,000 and 1,300 hours. Show your calculations