The graph shown represents a system of equations used to solve a polynomial inequality. If the polynomial expression must be greater than 50, which represents the solution set of the inequality? (–7, 0) U (2, ∞) (–7, –5.94) U (–2.469, 3.409) (–5.94, –2.469) U (3.409, ∞) (–5.94, –2.469) U (2, ∞)

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.