Question

In a study of brand recognition of Sony, groups of four consumers are interviewed. If xis the number of people in the group who recognize the Sony brand name, then xcan be 0, 1, 2, 3, or 4, and the corresponding probabilities are 0.0016, 0.0250, 0.1432, 0.3892, and 0.4096. Does the given information describe a probability distribution? Why or why not?

Short answer

The given information does not describe a probability distribution as the sum of the probabilities is not equal to 1.

Step-by-step solution

Given information

The data for the brand recognition of Sony by a group of four consumers is provided.

The variable x represents the number of people in the group who recognize the Sony brand name.

The feasible values of x are 0, 1, 2, 3, and 4, and the corresponding probabilities are 0.0016, 0.0250, 0.1432, 0.3892, and 0.4096.

Step 2: Check whether the given information describes a probability distribution

The requirements for a probability distribution table are as follows.

1) The variable x is a numerical random variable. In the given scenario, the variable is numerical as the values are in the form of numbers.

2) The sum of the probabilities is computed as

$$\begin{gathered} \sum P\left(x\right)=0.0016+0.0250+0.1432+0.3892+0.4096 \\ =0.9686 \end{gathered}$$

Therefore,the sum of the probabilities is not equal to 1.

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

Thus,the requirement that the sum of the probabilities should be 1 is not satisfied.

Therefore, the given information does not describe a probability distribution.