Question

In Exercises 7–14, determine whether a probability

distribution is given. If a probability distribution is given, find its mean and standarddeviation. If a probability distribution is not given, identify the requirements that are notsatisfied.

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 (based on data from “Hemispheric Dominance and Cell Phone Use,” by Seidman et al., JAMA Otolaryngology—Head &Neck Surgery,Vol. 139, No. 5).

	P(x)
Left	0.636
Right	0.304
No preference	0.06

Short answer

The requirement that x is a numerical random variable is not satisfied.

Step-by-step solution

Given information

The probability distribution for the ear that cell phone users use to hear their cell phone is provided.

Identify the requirements for a probability distribution

Let the variable x represents the ear that a cell phone user uses.

The requirements are as follows:

1)The variablex is not a numerical random variable as the variable cannot be numerically expressed.

2) The sum of the probabilities is computed as:

$$\begin{gathered} \sum P\left(x\right)=0.636+0.304+0.06 \\ =1 \end{gathered}$$

Therefore, the sum of the probabilities is 1.

3) Each value of P(x) is between 0 and 1.

Thus, the requirement that x is a numerical random variable is not satisfied.

Therefore, the mean and standard deviation cannot be computed.