The taste test for PTC (phenylthiocarbamide) is a favorite exercise in beginning human genetics classes. It has been established that a single gene determines whether or not an individual is a “taster.” If 70% of Americans are “tasters” and 20 Americans are randomly selected, what is the probability that

a at least 17 are “tasters”?

b fewer than 15 are “tasters”?

Solution:

Step 1 of 3:

Given,in a sample of 20 Americans, 70% of Americans are “tasters” .

Here, n = 20 and p = 0.70

We can use the Binomial distribution

Let X follows the Binomial distribution with probability mass function

P(X) = (, where, x = 0,1,2….,n