Final answer:
The variance of a binomial distribution with n = 25 and p = 0.85 is 3.1875 when rounded to four decimal places.
Step-by-step explanation:
The subject of this question is Mathematics, specifically dealing with the binomial distribution and the calculation of its variance. For a random variable x that follows a binomial distribution with parameters n = 25 and p = 0.85, the variance of x can be calculated using the formula σ^2 = npq. Here, q is the probability of failure, which is equal to 1 - p. Therefore, with n = 25 and p = 0.85, the variance (σ^2) is:
σ^2 = 25 × 0.85 × (1 - 0.85).
By calculation:
σ^2 = 25 × 0.85 × 0.15 = 3.1875.
Thus, the variance of the binomial distribution is 3.1875 when rounded to four decimal places.