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?
(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.