Question

The probability of reaching a certain point value in a popular video arcade game is listed in the table. Given that the table is a probability distribution, what is the mean, μ?

Answer 1

To calculate the mean (μ) of a discrete probability distribution, you can use the formula:

\[
\mu = \sum (x_i \cdot P(x_i))
\]

where \(x_i\) represents the point values and \(P(x_i)\) represents their corresponding probabilities.

Since you did not provide the specific table with point values and their probabilities, I’ll describe the steps to calculate the mean:

1. **List the Point Values and Probabilities**: You would identify the values of \(x_i\) (the scores) and \(P(x_i)\) (the probabilities of reaching those scores).

2. **Multiply Each Point Value by Its Probability**: For each point value, you would calculate \(x_i \cdot P(x_i)\).

3. **Sum All the Products**: Add all the values obtained from the multiplication together to find the mean.

4. **Result**: This sum gives you the mean μ of the probability distribution.

If you provide the actual data from your table, I would be happy to assist you further with the calculations!