4. You have joined the development team of a new search engine. You are in charge of analyzing the time taken to respond to a search query. The search time of the current algorithm is normally distributed, with mean 0.79 seconds and standard deviation 0.21 seconds. (a) (2 points) Let X be the algorithm's search time. Describe the distribution of X. (b) (2 points) According to the empirical rule, where do approximately 68% of the values fall? (c) (4 points) What is the probability that a random search takes more than 1.21 second to be responded? (d) (4 points) What is the probability that a random search is responded in more than 1.063 but less than 1.126 seconds? (e) (5 points) What is the value " of X such that 70 per cent of the searches take longer than a*