Question

groups of adults are randomly selected and arranged in groups of three. the random variable x is the number in the group who say that they would feel comfortable in a self - driving vehicle. determine whether a probability distribution is given. if a probability distribution is given, find its mean and standard deviation. if a probability distribution is not given, identify the requirements that are not satisfied.

does the table show a probability distribution? select all that apply.

a. yes, the table shows a probability distribution.
b. no, the sum of all the probabilities is not equal to 1.
c. no, the random variable x is categorical instead of numerical.
d. no, not every probability is between 0 and 1 inclusive.
e. no, the random variable xs number values are not associated with probabilities.

Explanation:

Step1: Check if \(x\) is numerical

The random variable \(x\) (number of people) is numerical. So option C is incorrect.

Step2: Check probability range

Each \(P(x)\) (0.362, 0.438, 0.176, 0.024) is between 0 and 1. So option D is incorrect.

Step3: Check sum of probabilities

$$
LATEXBLOCK0
$$

So option B is incorrect.

Step4: Check variable - probability association

Each value of \(x\) (0, 1, 2, 3) has an associated probability \(P(x)\). So option E is incorrect.

Answer:

A. Yes, the table shows a probability distribution.