Question

approximately 12% of all people are left - handed. consider 12 randomly selected people.
a) state the random variable.
select an answer
b) list the given numbers with correct symbols.
? = 12
? = 0.12
c) explain why this is a binomial experiment. check all that apply.
there is not a fixed number of people
whether or not one randomly selected person is left - handed will affect whether or not another randomly selected person is left - handed
p = 12% remains constant from one randomly selected person to another
there are only two outcomes for each person
there are more than two outcomes for each person
whether or not one randomly selected person is left - handed will not affect whether or not another randomly selected person is left - handed
there are a fixed number of people 12

Explanation:

Part (a)

The random variable here represents the number of left - handed people among the 12 randomly selected people. In a binomial experiment context, if we let \(X\) be the random variable, \(X\) can take values from 0 to 12, where each value represents the count of left - handed individuals in the sample of 12.

In a binomial experiment, \(n\) represents the number of trials (here, the number of people selected, which is 12), and \(p\) represents the probability of success (here, the probability that a person is left - handed, which is 12% or 0.12). So \(n = 12\) and \(p=0.12\).

1. A binomial experiment has a fixed number of trials. Here, we have 12 randomly selected people, so the number of trials \(n = 12\) is fixed. So the option "There are a fixed number of people, 12" is correct.
2. For each person, there are only two outcomes: either the person is left - handed (success) or right - handed (failure). So the option "There are only two outcomes for each person" is correct.
3. The probability of success \(p = 12\%\) remains the same for each randomly selected person. The handedness of one person does not affect the handedness of another, so the probability \(p\) is constant. So the option " \(p = 12\%\) remains constant from one randomly selected person to another" and "Whether or not one randomly selected person is left - handed will not affect whether or not another randomly selected person is left - handed" are correct. The options "There is not a fixed number of people" is wrong (we have \(n = 12\) fixed), "Whether or not one randomly selected person is left - handed will affect whether or not another randomly selected person is left - handed" is wrong (handedness is independent), and "There are more than two outcomes for each person" is wrong (only two outcomes: left - handed or right - handed).

Answer:

Let \(X\) be the number of left - handed people among the 12 randomly selected people.

Part (b)