Questions: Compute the probability of success using the binomial formula. Round your answer to three decimal places as needed.

Transcript text: Compute the probability of success using the binomial formula. Round your answer to three decimal places as needed.

Solution

Solution Steps

Step 1: Define the Problem

We are tasked with computing the probability of obtaining \( k \) or fewer successes in a binomial distribution scenario. Specifically, we want to find the probability of achieving 5 or fewer successes in 10 trials, where the probability of success on each trial is \( p = 0.5 \).

Step 2: Apply the Binomial CDF

The cumulative distribution function (CDF) for a binomial distribution gives us the probability of obtaining \( k \) or fewer successes. In this case, we calculate:

\[ P(X \leq 5) = 0.623 \]

This value represents the cumulative probability of achieving 5 or fewer successes in our defined binomial experiment.