Question 2 120 marks! In a factory producing batteries, there are two production lines, namely standard-quality and high-quality. According to the specications, lifetimes of batteries from the two production lines are as follow: Standard-quality: battery lifetime follows normal distribution with mean 1600 hours and standard deviation of 300 hours High-quality: battery lifetime follows normal distribution with mean 2000 hours and standard deviation of 125 hours. (a) Find the probability that a randomly chosen battery from standard-quality lasts for at least 1450 hours. (b) There are 53% of high-quality batteries with lifetime shorter than K hours. Find the value of K. (c) For many pairs of two randomly selected batteries, one from standard-quality and one from high-quality, what are the expectation and stande deviation of the total lifetime? (d) In a package with 9 randomly selected standard-quality batteries, what is the probability that at least 7 of the batteries lasts for at least 1450 hours