We are given a probability distribution table for the number of goals scored by a soccer player. We need to find the value of $P(1 \le x \le 3)$. The probability values for $x=0, 1, 2, 3, 4, 5$ are $0.07, 0.14, k, 0.46, 0.08, 0.02$ respectively.

1. Problem Description

We are given a probability distribution table for the number of goals scored by a soccer player. We need to find the value of $P(1 \le x \le 3)$. The probability values for $x=0, 1, 2, 3, 4, 5$ are $0.07, 0.14, k, 0.46, 0.08, 0.02$ respectively.

2. Solution Steps

First, we need to find the value of $k$. Since the sum of all probabilities in a probability distribution must equal 1, we have:

$0.07 + 0.14 + k + 0.46 + 0.08 + 0.02 = 1$

$0.77 + k = 1$

$k = 1 - 0.77$

$k = 0.23$

Now we need to find $P(1 \le x \le 3)$. This is equal to $P(x=1) + P(x=2) + P(x=3)$.

$P(1 \le x \le 3) = P(x=1) + P(x=2) + P(x=3) = 0.14 + k + 0.46$

Since $k=0.23$, we have

$P(1 \le x \le 3) = 0.14 + 0.23 + 0.46 = 0.83$

3. Final Answer

$0.83$