Questions: The random variable X is a binomial random variable with n=14 and p=0.2. What is the expected value of X? Do not round your answer.

Transcript text: The random variable $X$ is a binomial random variable with $n=14$ and $p=0.2$. What is the expected value of $X$ ? Do not round your answer.

Solution

Solution Steps

Step 1: Identify the Parameters of the Binomial Distribution

The problem states that the random variable $ X $ is a binomial random variable with parameters $ n = 14 $ and $ p = 0.2 $.

Step 2: Recall the Formula for the Expected Value of a Binomial Distribution

The expected value $ E(X) $ of a binomial distribution is given by the formula:

\[ E(X) = n \cdot p \]

Step 3: Calculate the Expected Value

Substitute the given values of $ n $ and $ p $ into the formula:

\[ E(X) = 14 \cdot 0.2 = 2.8 \]

Final Answer

The expected value of $ X $ is $\boxed{2.8}$.

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