Question

at a swim meet, juan noted the number of members on various swim teams. x is the number of swimmers that a randomly chosen team has. what is the expected value of x? write your answer as a decimal.

Explanation:

Step1: Calculate total number of teams

Total number of teams \(=2 + 4+4=10\)

Step2: Calculate probability for each number of swimmers

For \(62\) swimmers: \(P(X = 62)=\frac{2}{10}=0.2\)
For \(64\) swimmers: \(P(X = 64)=\frac{4}{10}=0.4\)
For \(71\) swimmers: \(P(X = 71)=\frac{4}{10}=0.4\)

Step3: Calculate expected value

The formula for expected value \(E(X)=\sum_{i}x_{i}P(x_{i})\)
\(E(X)=62\times0.2 + 64\times0.4+71\times0.4\)
\(=12.4+25.6 + 28.4\)
\(=66.4\)

Answer:

$66.5$