An srs of 400 high school seniors gained an average of ¯ x = 24.23 points in their second attempt at the sat mathematics exam. assume that the change in score has a normal distribution with standard deviation σ = 48.78 . we want to estimate the mean change in score μ in the population of all high school seniors.(a)give a 95% confidence interval for μ based on this sample.(b)based on your confidence interval in part (a), how certain are you that the mean change in score μ in the population of all high school seniors is greater than 0? (hint: does the interval in part (a) include