Let S represent the number of randomly selected adults in a community surveyed to find someone with a certain genetic trait.
The random variable S
follows a geometric distribution with mean 4.66. Which of the following is a correct interpretation of the mean?

A. A value randomly selected from the distribution of S
is expected to be 4.66.
A value randomly selected from the distribution of S is expected to be 4.66.

B. In repeated sampling from the distribution of S
, the average of the values will approach 4.66.
In repeated sampling from the distribution of S, the average of the values will approach 4.66.

C. For a sample of values randomly selected from the distribution of S
, the average of the sample will be 4.66.
For a sample of values randomly selected from the distribution of S, the average of the sample will be 4.66.

D. The probability is 0.66 that a value randomly selected from the distribution of S
will be close to the mean.
The probability is 0.66 that a value randomly selected from the distribution of S will be close to the mean.

E. For a sample of values randomly selected from the distribution of S
, the average of the sample will vary from the population mean by no more than 4.66.

The correct interpretation of the mean is in repeated sampling from the distribution of S, the average of the values will approach 4.66.

The Geometric distribution is a discrete probability distribution that shows the likelihood of the number of failures before the success attained.

Let consider S to be a random variable that represents the selected adults in a community surveyed.

Then

[tex]\mathbf{S \sim G(p) S = 4.66}[/tex]

Therefore, the correct interpretation of the mean is in repeated sampling from the distribution of S, the average of the values will approach 4.66.

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