Question 1 The frequency distribution of the 1-year total return for a random sample of investment funds is shown as below: 1-year total return (%) Frequency 20.0 but less than 25.0 3 25.0 but less than 30.0 13 30.0 but less than 35.0 24 35.0 but less than 40.0 11 40.0 but less than 45.0 4 45.0 but less than 50.0 5 (a) Calculate the mean of the 1-year total return. [3 marks] (b) Calculate the mode of the 1-year total return. [3 marks] (c) Calculate the standard deviation of the 1-year total return. [4 marks] (d) Based on the results obtained previously to calculate the Pearsons coefficient of skewness. [3 marks] (e) Estimate, from the frequency distribution table, the minimum among the highest 20% 1-year total return of investment funds. [4 marks] (f) Estimate, from the frequency distribution table, the proportion of investment funds with the 1-year total return between 28% and 38%. [4 marks] (g) Ten investment funds are randomly selected. Using the result of (f) to calculate the expected number of investment funds have the 1-year total return between 28% and 38%. [4 marks]