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. find the mean of the random variable x. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. μ = □ adult(s) (round to one decimal place as needed.) b. the table does not show a probability distribution.

Explanation:

Step1: Check if it is a probability distribution

For a table to be a probability distribution, two conditions must be met:

1. Each \(P(x)\geq0\).
2. \(\sum P(x) = 1\).

Here, \(0.362+0.438 + 0.176+0.024=1\) and all \(P(x)\) values are non - negative. So, it is a probability distribution.

Step2: Calculate the mean \(\mu\)

The formula for the mean of a discrete probability distribution is \(\mu=\sum xP(x)\).

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Answer:

A. \(\mu = 0.9\) adult(s)