To calculate the probability that the placekicker will make at least 4 out of his next 5 field goal attempts from the 20-yard line, we need to consider two cases:
1. The probability of making exactly 4 out of 5 field goals.
2. The probability of making all 5 out of 5 field goals.
The given table provides the probabilities for making exactly 0, 1, 2, 3, 4, or 5 field goals out of 5 attempts. We need to specifically focus on the probabilities for 4 and 5 successful attempts.
From the table:
- The probability of making exactly 4 out of 5 field goals is 0.392.
- The probability of making exactly 5 out of 5 field goals is 0.444.
To find the total probability of making at least 4 out of 5 field goals, we need to sum these two probabilities:
[tex]\[
P(\text{at least 4 out of 5}) = P(\text{exactly 4 out of 5}) + P(\text{exactly 5 out of 5})
\][/tex]
Substituting the values from the table, we get:
[tex]\[
P(\text{at least 4 out of 5}) = 0.392 + 0.444 = 0.836
\][/tex]
Therefore, the probability that the placekicker will make at least 4 of his next 5 attempts from the 20-yard line is:
[tex]\[
\boxed{0.836}
\][/tex]
