Phenylthiocarbamide, or PTC, is a molecule that tastes very bitter to those who can taste it. However, about 30% of people cannot taste it, due to a recessive allele in their DNA. Assume that the proportion with this genetic trait is exactly 30%. A researcher administers PTC to 15 randomly-selected subjects. Let X be the number of these subjects who are able to taste PTC.

(a) What is the probability distribution of X?

(b) Calculate:

(i) the mean and standard deviation of X.

(ii) P( X > 6)

(iii) P( 3 ≤ X ≤ 7)

(c) If 10 of the subjects could taste PTC, would this be an unusual sample? Justify your answer.