Final answer:
The probability P(x=5) for a binomial distribution with n=25 and p=0.2 can be calculated using the binomial probability formula or by a calculator function, such as binompdf(25, 0.2, 5) on a TI-83, 83+, or 84.
Step-by-step explanation:
The student is asking about how to calculate a probability for a specific value in a binomial distribution. For a binomial distribution where n represents the number of trials, and p is the probability of success in each trial, the probability of getting exactly x successes can be found using either the binomial probability formula directly or technology such as a calculator.
Since we are given n = 25 and p = 0.2, and we are asked to find P(x=5), we can use the binomial probability formula directly, or we can use a TI-83, 83+, or 84 calculator to compute this. To find this using the calculator, you would use the function binompdf(25, 0.2, 5) to get the probability.
The q is calculated as 1 - p, which is necessary for the calculation of the normal approximation if needed. However, for the exact binomial probability, this isn't required. Additionally, since n is sizable and p is within a reasonable range, the binomial distribution doesn't need to be approximated by a normal or Poisson distribution for this problem.