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

Explanation:

Step1: Check probability range

All probabilities \(P(x)\): \(0.193\), \(0.361\), \(0.349\), \(0.147\) are between \(0\) and \(1\) inclusive.

Step2: Check sum of probabilities

Calculate the sum \(S = 0.193+ 0.361+0.349 + 0.147=1\)

Step3: Check variable type

The random - variable \(x\) (number of students taking online courses) is numerical.
Since all requirements for a probability distribution are met, the table shows a probability distribution.

Answer:

A. Yes, the table shows a probability distribution