05 (15 points) The Colorall Paint factory uses "agent A" in the paint manufacturing process. There is an average of 3.45 particles of agent A in a cubic metre of the air emitted during the production process. (a) Let X = the number of particles of agent A in a cubic metre of the air emitted. What is the probability distribution of X? (b) What is the probability that there will be five particles of agent A in a cubic metre of air emitted from the factory? (c) What is the probability that there will be at least four particles of agent A in a cubic metre of air emitted from the factory? (d) Find the expected value, variance and the standard deviation of X. Q6 (15 points) The literacy rate for a nation measures the proportion of people age 15 and over who can read and write. The literacy rate for women in Afghanistan is 15%. Let X = the number of Afghani women you ask until one says that she is literate. (a) What is the probability distribution of X? (b) What is the probability that you ask six women before one says she is literate? (c) What is the probability that you must ask less than 4 women? (d) Find the mean, variance and standard deviation of X