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

Explanation:

Step1: Check requirements for probability distribution

A probability distribution has a random - variable \(x\) which is numerical and the sum of all probabilities \(P(x)\) must be 1, and each \(P(x)\) must be between 0 and 1 inclusive. Here, the random variable \(x\) (left, right, no preference) is categorical.

Step2: Analyze sum of probabilities

\(0.6354 + 0.3043+0.0596=0.9993
eq1\)

Answer:

B. No, the random variable x is categorical instead of numerical
C. No, the sum of all the probabilities is not equal to 1