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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"?

Answer :

Answer:

(a) 0.1071

(b)  0.4164 .

Step-by-step explanation:

We are given that a single gene determines whether or not an individual is a "taster." 70% of Americans are "tasters" and 20 Americans are randomly selected.

We can take this situation as of Binomial distribution i.e.;

       [tex]P(X=x) = \binom{n}{x}p^{x}(1-p)^{n-x} ; x = 0,1,2,3,....[/tex]

 where, n = number of trials or number of samples

              x = required success

              p = probability of success

So, here success is that gene determines individual to be a "taster." i.e.

p = 0.70 and also n = 20

(a) Probability that at least 17 are "tasters" = P(X >= 17)

   For this we will use binomial probabilities table in which less than probabilities are given so;

    P(X >= 17) = 1 - P(X <=16) = 1 - 0.8929 = 0.1071.

(b) Probability that fewer than 15 are "tasters" = P(X < 15)

           P(X < 15) = P(X <= 14) = 1 - 0.5836 = 0.4164 .

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