A restaurant manager tracks the number of people in every party to sit at a specific table every day for a week, and then compiles the results into a probability distribution as shown in the table: Number of People , X 12 34 6 Relative Frequency, P(X) 0.05 0.18 0.22 0.06 0.03
To find the expected value of the distribution, we use the formula:
E(X) = Σ[X * P(X)]
where Σ represents the sum over all possible values of X.
Using the table given, we plug in the values for X and P(X) to get:
E(X) = (12 * 0.05) + (34 * 0.18) + (6 * 0.22) + (4 * 0.06) + (3 * 0.03)
E(X) = 0.6 + 6.12 + 1.32 + 0.24 + 0.09
E(X) = 8.37
Therefore, the expected value for the number of people in a party at this specific table is 8.37.