Part A 1. Suppose X1 is normally distributed with a mean of 3 and a standard deviation of 1 and suppose I; is normally.r distributed with a mean of 5 and a standard deviation of 2. [a] For independent samples of sizes 3 and 10. respectively. nd the mean and standard deviation of X1 X3. [3 marks] [b] Would your answers in [a] change if X1 and for I; were not normally distribute d? Explain your answer. [2 marks] [c]: Explain why X1 X3 is normally distributed. :_ies_p_it_e_tl_1e_fa_ot_th_a1: both ml and n2 are small. [2 marks] [:1] Suppose two independent samples are randomly obtained from populations 1 and 2. with sample sizes n1 2 B and n2 2 10. Compute the probability that either sample average is at least 3 greater than the other. [5 marks]