Final answer:
The question pertains to finding the probability of 18 or fewer successes in a binomial distribution with 72 trials and a success probability of 0.25. The solution involves using a binomial CDF with parameters 72, 0.25, and 18, which can be calculated using a statistical calculator or software.
Step-by-step explanation:
The student's question revolves around a binomial distribution with a specific number of trials and a given probability of success. The distribution parameters described are 72 trials with a 0.25 probability of success, and we need to find the probability of achieving 18 or fewer successes (X ≤ 18). The appropriate method to solve this problem involves using a binomial cumulative distribution function (CDF).
Here are the steps to find the binomial probability:
- Identify the number of trials (n) and the probability of success (p), which in this case are 72 and 0.25, respectively.
- Compute q as 1 - p to find the probability of failure for one trial. In this case, q = 1 - 0.25 = 0.75.
- Use a statistical calculator or software with a binomial CDF function to calculate the probability of X being 18 or fewer. The CDF function syntax would generally resemble binomcdf(72, 0.25, 18).
- The result from step 3 will give the probability of obtaining 18 or fewer successes in 72 trials with a success probability of 0.25.
To solve this problem accurately, we'd use a calculator or software to find binomcdf(72, 0.25, 18), and it will provide the probability value required.