Question 1 (a) The scores of a test for a group of 5 students are 50, 63, 77, 82, and 91. (i) Construct the sampling distribution of the mean of the score for samples of size 3 by filling in the following two tables. [8 marks] No Sample Sample mean . .. Sample mean Frequency Probability of sample mean (ii) Show that the mean of the sampling distribution of the sample mean equals the mean of the population. [2 marks] (b) Car batteries have a life span that is normally distributed with a mean and standard deviation of 24 months and 12 months, respectively. Use only the table provided in the appendix to find any related probability value. (i) Find the probability that the mean life span of a random sample of 20 car batteries falls between 28 and 30 months. [5 marks] (ii) A random sample of 50 car batteries is obtained. The probability that this sample has a mean life span more than k months is 0.15. Find the value of k. [5 marks]