Questions: Fill in the missing value so that the following table represents a probability distribution. x 5 6 7 8 P(x) 0.1 square 0.3 0.3 square

Solution Steps

We have the following values and their corresponding probabilities:

\[ \begin{array}{c|cccc} x & 5 & 6 & 7 & 8 \\ \hline P(x) & 0.1 & \square & 0.3 & 0.3 \end{array} \]

To ensure that the table represents a valid probability distribution, the sum of all probabilities must equal 1. We can express this mathematically as:

\[ P(5) + P(6) + P(7) + P(8) = 1 \]

Substituting the known values:

\[ 0.1 + P(6) + 0.3 + 0.3 = 1 \]

This simplifies to:

\[ P(6) + 0.7 = 1 \]

Solving for \( P(6) \):

\[ P(6) = 1 - 0.7 = 0.3 \]

The missing probability \( P(6) \) is:

\[ P(6) = 0.3 \]

Final Answer