2. The birth weight of 260 rat-pups were recorded and are stored in the Excel file called Birth Weight.xlsx which can be downloaded from LMS. The data consists of a single column with the heading "Birth Weight". You are required to use Excel to answer the questions below and we will treat this data as population data for this question. (a) Calculate the population average of the birth weights provided in the Excel file. What is the population average and what was the Excel formula that you used to calculate it? (3 marks) (b) Calculate the population median of the birth weights provided in the Excel file. What is the population median and what was the Excel formula that you used to calculate it? (3 marks) (c) Calculate the population standard deviation of the birth weights provided in the Excel file. What is the population standard deviation and what was the Excel formula that you used to calculate it? (3 marks) (d) The empirical rule in statistics states, that if the data in the population is approximately normally dis- tributed then approximately 95% of the values in a population should fall within the interval 20 (where and are the population average and population standard deviation respectively). (i) If the birth weights of the rat-pups are approximately normally distributed then how many of the 260 values would you expect to fall within the interval 20? Explain how you arrived at your answer. (1 mark) (ii) How many of the 260 birth weights in the Excel file fall within the interval 2? Explain how you arrived at your answer. NOTE: there are several ways to do this. If you are not sure how then try searching the internet which has many forums etc. that can be helpful for problems such as this. (2 marks) (iii) What percentage of the 260 birth weights fall within the interval 20? Make sure you show all your workings. (2 marks) (iv) Do you think there is evidence to suggest that the birth weights of the rat-pups are approximately normally distributed? Explain.