Question

A sociologist randomly selects single adults for different groups of​ three, and the random variable x is the number in the group who say that the most fun way to flirt is in person. 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. x ​P(x) 0 0.087 1 0.328 2 0.416 3 0.169 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's number values are not associated with probabilities. C. ​No, the random variable x is categorical instead of numerical. D. ​No, the sum of all the probabilities is not equal to 1. E. ​No, not every probability is between 0 and 1 inclusive.

Answer 1

A. ​Yes, the table shows a probability distribution.

Explanation:

In a probability distribution, none of the values can be negative or over 1. Additionally, all of the values must sum to 1.

Our probabilities are:

0.087; 0.328; 0.416; and 0.169. None of these are negative and none are over 1.

0.087+0.328+0.416+0.169 = 1.00; this means that this is a probability distribution.