Question

A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite. The geologist instructs a laboratory assistant to randomly select 15 of the speci- mens for analysis. a. What is the pmf of the number of granite specimens selected for analysis

Answer 1

Thus, the pmf of the number of granite specimens selected for analysis is
`P(X=x)={20\choose x}0.50^(x)(1-0.50)^(20-x)`.

Explanation:

The experiment consists of collecting rocks.

The sample consisted of, 10 specimens of basaltic rock and 10 specimens of granite.

The total sample is of size, n = 20.

Let the random variable X be defined as the number of granite specimen selected.

The probability of selecting a granite specimen is:

`P(Granite)=p=(10)/(20)=0.50`

A randomly selected rock can either be basaltic or granite, independently.

The success is defined as the selection of granite rock.

The random variable X follows a Binomial distribution with parameter n = 20 and p = 0.50.

The probability mass function of X is:

`P(X=x)={20\choose x}0.50^(x)(1-0.50)^(20-x)`