2. [12 marks] In Australia, 30% of the population has blood type A+. Consider X, the...

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2. [12 marks] 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? (b) Calculate: (i) the mean and standard deviation of X. (ii) P(X > 12) (iii) P(5 X < 10) 3 [3] [3] [2] [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] 2. [12 marks] 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? (b) Calculate: (i) the mean and standard deviation of X. (ii) P(X > 12) (iii) P(5 X < 10) 3 [3] [3] [2] [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]