Question

Researchers are concerned about the rise in drinking behaviors among adolescents aged 13-17 in a particular community. Suppose the research team estimates the prevalence of such behaviors is 17%. A sample of 12 adolescents in this age range is collected. Let X represent the number of individuals in the sample with presence of this behavior. The probability of seeing no cases in a sample is 0.2627 0.0421 1 0.1069 None of the other choices represents a suitable response

Researchers are concerned about the rise in drinking behaviors among adolescents aged 13-17 in a particular community. Suppose the research team estimates the prevalence of such behaviors is 17%. A sample of 12 adolescents in this age range is collected. Let X represent the number of individuals in the sample with presence of this behavior.

• The probability of seeing no cases in a sample is

		0.2627
		0.0421
		1
		0.1069
		None of the other choices represents a suitable response

Answer 1

The same can be treated as a Binomial because:

(1)There are a fixed number of trials = 12.

(2) The process is random (given)

(3) There are only 2 outcomes. These outcomes are mutually exclusive.

(4) The trials is independent of the other and

(5) The probability of each trial remains the same from trial to trial.

Please note ^nC_r = \frac{n!}{(n-r)! * r!}

Binomial Probability = ⁿC_x * (p)^x * (q)^n-x, where n = number of trials and x is the number of successes.

Here n = 12, p = 0.17, q = 1 – p = 0.83.

P(X = 0) = ¹²C₀ * (0.17)⁰ * (0.83)^12-0 = 0.1069 Option 3