You volunteer with the Students Union and work closely with the Communications Officer. You have studied Statistics in college and believe that your understanding of statistics could be of use to the Union and its members. To show how statistical methods could be used you have taken some real-world problems and addressed them using a variety of statistical techniques. Prepare a report for the Communications Officer that addresses the following: Problem 1 (20 marks) A. The Students Union has carried out a survey of how many hours a week a group of 40 students spend on campus. The table below gives the number of on-campus hours per week for 8 of these students. 12.0 15.0 17.0 19.0 22.0 8.0 11.0 20.0 Calculate the Standard Deviation of the above data using the relevant Method 1 and Method 2 formulae for variance (7.5 marks) Continues next page B. The Students Union Caf asked the 5 customers who were in the caf yesterday between 2.00 pm and 3.00 9m how many minutes they spent in the cafe during an average visit. Their answers are below 15.0 22.0 31.0 16.0 40.0 Calculate the Standard Deviation of the above data using the relevant Method 1 and Method 2 formulae for variance (7.5 marks) C. Outline what percentage of student exam results should be within (i) 2 standard deviations of the mean, and (ii) 3 standard deviations of the mean (2 marks) D. Outline 3 characteristics of a 'Normal Distribution' (3 marks)