Question

a kicker for a football team makes field goals 85% of the time when kicking from the 20 - yard line. assume that field - goal attempts can be considered random events. using the table, what is the probability that the placekicker will make at least 4 of his next 5 attempts from the 20 - yard line?

0.392
0.444
0.556
0.836

Explanation:

Step1: Calculate the probability of making 5 field - goals

Since the sum of all probabilities in a probability distribution is 1. Let \(P(5)=x\). Then \(0.00008 + 0.002+0.024 + 0.138+0.392+x = 1\).

$$x=1-(0.00008 + 0.002+0.024 + 0.138+0.392)$$

$$x = 1 - 0.55608=0.44392\approx0.444$$

Step2: Calculate the probability of making at least 4 field - goals

The probability of making at least 4 field - goals is \(P(X\geq4)=P(4)+P(5)\).
We know \(P(4) = 0.392\) and \(P(5)\approx0.444\) (from Step 1).

$$P(X\geq4)=0.392 + 0.444$$

Answer:

\(0.836\)