Question

college students are randomly selected and arranged in groups of three. the random variable x is the number in the group who say that they take one or more online courses.
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, not every probability is between 0 and 1 inclusive.
c. no, the sum of all the probabilities is not equal to 1.
d. no, the numerical values of the random variable x are not associated with probabilities.
e. no, the random variable x is categorical instead of numerical.
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=□ students
(round to one decimal place as needed.)
b. the table does not show a probability distribution.

Explanation:

Step1: Check probability distribution conditions

For a table to be a probability distribution:

1. Every \(P(x)\) must be between \(0\) and \(1\) (inclusive).
2. \(\sum P(x)=1\).

Here, \(0\leq0.108\leq1\), \(0\leq0.357\leq1\), \(0\leq0.388\leq1\), \(0\leq0.147\leq1\).
And \(\sum P(x)=0.108 + 0.357+0.388 + 0.147=1\). So, the table shows a probability distribution.

Step2: Calculate the mean \(\mu\)

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

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Answer:

A. Yes, the table shows a probability distribution.
A. \(\mu = 1.6\) students