Assume the function f is differentiable over the interval (-infinity, infinity). classify the following statement as either true or false. if the statement if false, explain why. if f has exactly two critical values at x = a and x = b, where a < b, then there must exist exactly one point of inflection at x = c such that a < c < b. in other words, exactly one point of inflection must exist between any two critical values. select the correct choice below. a. the statement is true b. the statement is false. there can be multiple inflection points between two critical values c. the statement is false. no infection points can exist between two critical values. any potential inflection points will be either less than the smallest critical value or greater than the largest critical value d. the statement is false. inflection points always exist in pairs, so two inflection points must exist between the two critical values.

(20 points) a bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. the bank prides itself on its mortgage application process and decides to investigate the claims. the bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times (in days): 5, 7, 22, 4, 12, 9, 9, 14, 3, 6, 5, 15, 10, 17, 12, 10, 9, 4, 10, 13 assume that the random variable x measures the number of days a customer waits for mortgage processing at this bank, and assume that x is normally distributed. 2a. find the sample mean of this data (x ě…). 2b. find the sample variance of x. find the variance of x ě…. for (c), (d), and (e), use the appropriate t-distribution 2c. find the 90% confidence interval for the population mean (îľ). 2d. test the hypothesis that îľ is equal to 7 at the 95% confidence level. (should you do a one-tailed or two-tailed test here? ) 2e. what is the approximate p-value of this hypothesis?