In Australia, 30% of the population has a 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)

(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.