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, not every probability is between 0 and 1 inclusive. 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, the random variable x is categorical instead of numerical.

Explanation:

Step1: Check probability range

All probabilities \(P(x)\) (0.6361, 0.3038, 0.0601) are between 0 and 1 inclusive.

Step2: Check sum of probabilities

Calculate the sum: \(0.6361 + 0.3038+0.0601=1\)

Step3: Check variable type

Although the random variable \(x\) (Left, Right, No preference) is categorical, for the purpose of checking if it is a probability distribution (the main requirements are non - negative probabilities summing to 1), it still satisfies the criteria of a probability distribution.

Answer:

A. Yes, the table shows a probability distribution.