The taste test for PTC (phenylthiourea) is a common class demonstration in the study of genetics. It is know that 70% of the American population are "tasters" and 30% are "non-tasters". Suppose a genetics class of size 20 does the test to see if they match the U.S. percentages of "tasters" and "non-tasters". Assume the assignment of students to classes is a random process.

a.) Write the expression for P(X = 15 tasters) using pk(1-p)n-k notation.

b.) Use your calculator to evaluate the expression in a.).

c.) Using the notation in part a.), write out all of the probabilities need to evaluate P(X < 5 non-tasters). Use your calculator to evaluate the probability.

d.) Explain what probabilities you would use to evaluate P(3 < X < 9)