A brother and a sister are in the same math class. There are 8 boys in the class and there are 10 girls in the class. If one boy and one girl are chosen at random, what is the probability that the brother and sister will be the two students chosen? Answer as a fraction.

Arandom sample of n = 25 observations is taken from a n(µ, σ ) population. a 95% confidence interval for µ was calculated to be (42.16, 57.84). the researcher feels that this interval is too wide. you want to reduce the interval to a width at most 12 units. a) for a confidence level of 95%, calculate the smallest sample size needed. b) for a sample size fixed at n = 25, calculate the largest confidence level 100(1 − α)% needed.