Suppose an urn contains seven chips labeled 1, . . . , 7. Three of the chips are black, two are red, and two are green. The chips are drawn randomly one at a time without replacement until the urn is empty. (a) What is the probability that the i th draw is chip number 5? (b) What is the probability that the i th draw is black?

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.