Question

approximately 11% of all people are left - handed. consider 17 randomly selected people.
a) state the random variable.
rv x = the number of 17 randomly selected people that are left - handed
b) list the given numbers with correct symbols.
? = 17
p = 0.11
c) explain why this is a binomial experiment. check all that apply.
p = 11% remains constant from one randomly selected person to another
there is not a fixed number of people
there are only two outcomes for each person
there are more than two outcomes for each person
there are a fixed number of people, 17
whether or not one randomly selected person is left - handed will affect whether or not another randomly selected person is left - handed
whether or not one randomly selected person is left - handed will not affect whether or not another randomly selected person is left - handed

Explanation:

Step1: Identify the binomial - experiment criteria

A binomial experiment has the following properties: fixed number of trials ($n$), two possible outcomes per trial, probability of success ($p$) is constant for each trial, and the trials are independent.

Step2: Analyze the given situation

We have $n = 17$ (fixed number of people selected). The probability $p=0.11$ (probability of a person being left - handed) is constant for each person. Each person is either left - handed (success) or not left - handed (failure), so there are two outcomes per person. Also, the handed - ness of one person does not affect the handed - ness of another person.

Answer:

• p = 11% remains constant from one randomly selected person to another: True
• There is not a fixed number of people: False
• There are only two outcomes for each person: True
• There are more than two outcomes for each person: False
• There are a fixed number of people, 17: True
• Whether or not one randomly selected person is left - handed will affect whether or not another randomly selected person is left - handed: False
• Whether or not one randomly selected person is left - handed will not affect whether or not another randomly selected person is left - handed: True