Question

The taste test for PTC (phenylthiourea) is a common class demonstration in the study of genetics. It is known that 70% of the American people are "tasters" with the rest are "non-tasters". Suppose a genetics class of size 20 does the test to see if they match the American percentage of "tasters" and "non-tasters". Assume that the assignment of students to classes is a random process. Calculate the variance.

Answer 1

Answer:

The variance for the number of tasters is 4.2

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they are tasters, or they are not. The probability of a person being a taster is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The variance of the binomial distribution is:

$V(X) = np(1-p)$

It is known that 70% of the American people are "tasters" with the rest are "non-tasters". Suppose a genetics class of size 20

This means that $p = 0.7, n = 20$

So

$V(X) = np(1-p) = 20*0.7*0.3 = 4.2$

The variance for the number of tasters is 4.2