6. . An iid sample of in. observations is drawn from a population with mean equal to 20 and standard deviation equal to 16. Let X be the sample mean. (a) Given to. = 8/1. Approximate P(X 0.5 is at most 0.05? Installation of some software package requires downloading 82 les. On average, it takes 15 seconds to download one le, with a variance of 16 seoz. What is the (approximate) probability that the software is installed in less than than 20 minutes? (Use the Central Limit Theorem) . Suppose the installation time in hours for a software on a laptop has probability density function f X (:r) : (1x3), f} g :r: g 1. (a) Find the probability that the software takes less than 0.50 hours to be installed on your laptop. (b) Let X1. ...,X3U be the installation times of the software on 30 different laptops. Assume the installation times are independent. Find the probability that the average installation time is shorter than {1.50 hours. Cite the theorem you use