Question

cengage webassign - 2020-sp-math-1401-co3 elementary statistics section co3 spring 2020 co
the world bank records the prevalence of hiv in countries around the world. according to their data, \prevalence of hiv refers to the percentage of people ages 15 to 49 who are infected with hiv.\ in one country, the prevalence of hiv is 18.5%. let
x = the number of people you test until you find a person infected with hiv
part (a)
sketch a graph of the distribution of the discrete random variable x
part (b)
part (c)

Explanation:

Step1: Identify distribution type

$X$ follows a geometric distribution, which models the number of trials until the first success. For a geometric distribution, the probability mass function is $P(X=x) = (1-p)^{x-1}p$, where $p=0.185$ (HIV prevalence).

Step2: Analyze probability trend

As $x$ (number of trials) increases, $(1-p)^{x-1}$ decreases exponentially, so $P(X=x)$ decreases as $x$ increases. This means the tallest bar is at $x=1$, with each subsequent bar being shorter.

Answer:

The correct graph is the bottom-right one, where the probability $P(X=x)$ starts highest at $x=1$ and decreases steadily as $x$ increases.