1. (a) Compute the first (Q1), the median (Q2) and the 75th percentile P75 hence find the interquartile range for the following data. 178.0 215.0 174.0 153.0 176.0 232.0
(b) Let X be a random variable representing the amount of water in liters used (lavatory, drinking and hand washing) by an individual University staff per day. Suppose that X>N(40,4.46) AND THAT A SAMPLE OF SIZE 50 IS TAKEN FROM THIS DISTRIBUTION. (
(i) Find the probability that if a staff member is randomly picked from the sample, he/she consumes between 37.9 and 39.8 liters.
(ii) What is the probability that the mean consumption of this sample exceeds 40.5 liters?
(c) Define the term series and state three main reasons for the time series analysis
State the conditions required for the chi-square results to be valid and how such conditions may overcomes in case they are violent.
(d) Use the sample data below from a certain population to answer the questions that follows.
37.3 44.3 41.4 37.2 41.5 42.8 47.4 47.6 46.6 41.3 46.4 37.9
(i) The mean of the sample and that of the population
(ii) The variance of the sample and that of the population
(iii) State and test at a=0.05 the chain that the population