Question

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. 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, the sum of all the probabilities is not equal to 1 e. no, not every probability is between 0 and 1 inclusive. 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 = (round to one decimal place as needed.) b. the table does not show a probability distribution. find the standard deviation of the random variable x. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Explanation:

Step1: Check probability - distribution requirements

1. The probabilities \(P(x)\): \(0.0363\), \(0.3037\), \(0.060\) are all between \(0\) and \(1\) inclusive.
2. Calculate the sum of probabilities: \(0.0363 + 0.3037+0.060=0.4

eq1\).

1. The random - variable \(x\) (left, right, no preference) is categorical. A probability distribution requires a numerical random variable.

Step2: Determine if it's a probability distribution

Since the random variable \(x\) is categorical instead of numerical and the sum of probabilities is not equal to \(1\), it is not a probability distribution.

Answer:

B. No, the random variable x is categorical instead of numerical
D. No, the sum of all the probabilities is not equal to 1
B. The table does not show a probability distribution
B. The table does not show a probability distribution