The mass of coffee in a randomly chosen jar sold by a certain company may be taken to have a normal distribution with means 203 g and standard deviation 2.5g. (i) Find the probability that a randomly selected jar will contain at least 200g of coffee. (ii) Obtain the probability that two randomly selected jars will together contain between 400g and 405g of coffee. (iii) The random variable C denotes the mean mass (in grams) of coffee per jar in a random sample of 20 jars. Identify the value of a such that P(C – 203 < a) = 0.95.

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