When Kayden commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 54 minutes and a standard deviation of 4 minutes. Using the empirical rule, determine the interval that represents the middle 99.7% of his commute times.

I’ve been trying all day to figure this puzzle out. i need the work for it aswell. it is a factoring polynomials tarsia. the image is below.

Which statement is true about the extreme value of the given quadratic equation? a. the equation has a maximum value with a y-coordinate of -21. b. the equation has a maximum value with a y-coordinate of -27. c. the equation has a minimum value with a y-coordinate of -21. d. the equation has a minimum value with a y-coordinate of -27.

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.