Question

Spell-checking Refer to Exercise 3. Calculate the mean of the random variable X and interpret this result in context.

Short answer

On average there are $2.1$ nonword errors in a $250$-word essay.

Step-by-step solution

Given Information

The number $X$ of nonword errors has the following distribution:

Explanation

The sum of each alternative multiplied by its likelihood is the expected value:

$$\begin{gathered} E\left(X\right)=\sum xP\left(x\right) \\ =0\times 0.1+1\times 0.2+2\times 0.3+3\times 0.3+4\times 0.1 \\ =2.1 \end{gathered}$$

This suggests that in a $250$-word essay, there are on average $2.1$ nonword errors.