[NW] [DATA] TelevisionsIn the Sullivan Statistics Survey I, individuals were asked to disclose the number of televisions in their household. In the following probability distribution, the random variable X represents the number of televisions in households.

e. What is the probability that a randomly chosen household has three televisions?

Verified step by step guidance

1. Identify the random variable X, which represents the number of televisions in a household.
2. Locate the value of X for which you want to find the probability, which is 3 televisions in this case.
3. Look up the corresponding probability P(x) for X = 3 in the given probability distribution table.
4. The probability that a randomly chosen household has three televisions is the value of P(3) from the table.
5. Express the probability as P(X = 3) = 0.176, based on the table data.

Key Concepts

Probability Distribution

A probability distribution lists all possible values of a random variable along with their associated probabilities. It shows how the total probability of 1 is distributed among different outcomes, helping to understand the likelihood of each event.

Random Variable

A random variable is a numerical outcome of a random phenomenon. In this case, the random variable X represents the number of televisions in a household, and it can take values from 0 to 9, each with a specific probability.

Interpreting Probability from a Table

To find the probability of a specific event, such as having three televisions, locate the value of the random variable in the table and read its corresponding probability. This direct lookup method simplifies answering probability questions.