Final answer:
The expected value of the number of days per week that a men's soccer team plays soccer is 1.1 days, calculated as a weighted average of the possible outcomes given their respective probabilities.
Step-by-step explanation:
To find the long-term average or the expected value (also denoted as μ) of the number of days per week that a men's soccer team plays soccer, one must calculate the weighted average of all possible outcomes. In this context, the outcomes are the number of days played per week by the team (0, 1, or 2 days), each having a corresponding probability (0.20, 0.50, and 0.30 respectively).
Let X represent the random variable for the number of days the men's soccer team plays soccer per week. To compute the expected value E(X), use the formula μ = E(X) = Σ xP(x), where x is a value that the random variable can take on, and P(x) is the probability of x occurring.
The calculation will be as follows: μ = (0 × 0.20) + (1 × 0.50) + (2 × 0.30) = 0 + 0.50 + 0.60 = 1.1.
Therefore, the expected value is 1.1. This means the men's soccer team can expect to play soccer, on average, 1.1 days per week in the long-term.