Question

according to a recent survey, 47 percent of the people living in a certain region carry a certain genetic trait. people from the region will be selected at random one at a time until someone is found who carries the genetic trait. let the random variable g represent the number of people selected to find one person who carries the genetic trait. on average, how many people from the region will need to be selected to find one person who carries the genetic trait?
a 0.47
b 0.69
c 1.55
d 2.00
e 2.13

Explanation:

Step1: Identify the distribution

The random variable \( G \) follows a geometric distribution because we are counting the number of trials (people selected) until the first success (finding a person with the genetic trait). For a geometric distribution, the probability of success \( p \) is the probability that a person carries the genetic trait. Here, \( p = 0.47 \) (since 47% of people carry the trait).

Step2: Recall the mean of a geometric distribution

The mean (expected value) of a geometric distribution is given by the formula \( \mu = \frac{1}{p} \), where \( p \) is the probability of success on a single trial.

Step3: Calculate the mean

Substitute \( p = 0.47 \) into the formula: \( \mu = \frac{1}{0.47} \approx 2.13 \).

Answer:

E. 2.13