To find the probability that the placekicker will make at least 4 of his next 5 attempts from the 20-yard line, we'll consider the probabilities for making exactly 4 and exactly 5 field goals.
First, let's look at the probabilities given in the table:
- The probability of making exactly 4 field goals is 0.392.
- We need to determine the probability of making exactly 5 field goals.
### Step-by-Step Explanation:
1. Extract the Given Information:
- The probability of making exactly 4 field goals out of 5 is [tex]\( P(4) = 0.392 \)[/tex].
- The total number of attempts is [tex]\( n = 5 \)[/tex].
- The probabilities for making fewer than 4 field goals are provided but are not directly necessary for calculating the desired outcome.
2. Probability of Making Exactly 5 Field Goals:
- The given problem requires the probability of making at least 4 out of 5 attempts.
- [tex]\( P(5) = 0.444 \)[/tex] is the probability of making 5 field goals.
3. Summing the Probabilities:
- The probability of making at least 4 out of 5 is the sum of the probabilities of making exactly 4 and exactly 5 field goals.
- Thus, we need to add [tex]\( P(4) \)[/tex] and [tex]\( P(5) \)[/tex].
[tex]\[
P(\text{at least 4}) = P(4) + P(5) = 0.392 + 0.444 = 0.836
\][/tex]
4. Conclusion:
- Therefore, the probability that the placekicker will make at least 4 of his next 5 attempts from the 20-yard line is:
[tex]\[
0.836
\][/tex]
This matches one of the choices provided. The correct answer is indeed:
[tex]\[
0.836
\][/tex]
