Q1. Building Confidence Intervals. The 90th percentile confidence interval for the number of active connections on a web server is given by the interval [15 1.5]. This confidence interval was computed using 36 observations of the web server. Answer the following questions (stating any assumptions you make): (1) What is the standard deviation of the sample used to compute this confidence interval was? (2) What is the probability that the true mean of the number of active connections on the web server is larger than 16? (3) Using the 36 observations, compute the 99th percentile confidence interval for the number of active connections on the web server. (4) If you double the number of observations, what would you expect the error in the 90th percentile confidence interval to be? What assumption did you have to make to give that answer? (5) How many additional observations do you need to make in order to make the error in the 90th percentile confidence be less than 5%? What assumption did you have to make to give that answer?