In a survey, cell phone users were asked which ear they use to hear their cell phone, and the table is based on their responses. 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 \begin{tabular}{|l|c|} \hline & $P(x)$ \\ \hline Left & 0.6356 \\ \hline Right & 0.3042 \\ \hline \begin{tabular}{l} No \\ preference \end{tabular} & 0.0602 \\ \hline \end{tabular} 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, not every probability is between 0 and 1 inclusive. E. No, the random variable $\mathrm{x}$ is categorical instead of numerical

Step 1 ：First, we need to check if the table shows a probability distribution. For a table to show a probability distribution, it must satisfy the following conditions: 1. The sum of all the probabilities must be equal to 1. 2. Every probability must be between 0 and 1 inclusive. 3. The numerical values of the random variable x are associated with probabilities. 4. The random variable x can be categorical or numerical.

Step 2 ：Let's check these conditions one by one. The probabilities given are 0.6356, 0.3042, and 0.0602. The sum of these probabilities is 1.0, and all probabilities are between 0 and 1 inclusive. So, the first two conditions for a probability distribution are satisfied.

Step 3 ：The third condition is that the numerical values of the random variable x are associated with probabilities. In this case, the random variable x is categorical (Left, Right, No preference) and each category is associated with a probability. So, the third condition is also satisfied.

Step 4 ：The fourth condition is that the random variable x can be categorical or numerical. In this case, the random variable x is categorical, which is allowed. So, the fourth condition is also satisfied.

Step 5 ：Therefore, the table shows a probability distribution. The final answer is \(\boxed{\text{A. Yes, the table shows a probability distribution.}}\)