In Australia, 30% of the population has blood type A+. Consider X, the number having A+ blood among 18 randomly-selected Australians. (a) What is the probability distribution of X? [3] (b) Calculate: (i) the mean and standard deviation of X. [3] (ii) P(X > 12) [2] (iii) P(5 X < 10) [2] (c) If, in such a sample, you found only 5 people with A+ blood, would this be an unusual sample? Justify your answer using an appropriate probability calculation. [2] 3. [3 marks] Suppose the random variable, Y, has the probability distribution, Y 1 2 3 P(Y = y) 0.57 0.27 0.16 (a) Calculate the mean, and [1] (b) the standard deviation [2