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

Explanation:

Step1: Check sum of probabilities

Sum \(P(x)=0.101 + 0.353+0.404 + 0.142\)
\(=0.101+0.353 + 0.404+0.142=1\)

Step2: Check range of probabilities

All probabilities \(0.101,0.353,0.404,0.142\) are between \(0\) and \(1\) inclusive. Also, \(x = 0,1,2,3\) are numerical values and are associated with probabilities.

Answer:

A. Yes, the table shows a probability distribution