Step 1 :A binomial probability experiment is conducted with the parameters \(n=9\), \(p=0.8\), and we are asked to compute the probability of \(x \leq 3\) successes.
Step 2 :We calculate the probability for each value of \(x\) in the range 0 to 3 using the binomial probability mass function (pmf).
Step 3 :The calculated probabilities for \(x=0\), \(x=1\), \(x=2\), and \(x=3\) are approximately \(5.12 \times 10^{-7}\), \(1.84 \times 10^{-5}\), \(0.000294912\), and \(0.002752512\) respectively.
Step 4 :We sum these probabilities to get the total probability of \(x \leq 3\).
Step 5 :The total probability is approximately \(0.003066368\).
Step 6 :We round this to four decimal places as needed, giving a final answer of \(\boxed{0.0031}\).