Deer mice (Pemmyscus maniculatus) are small rodents native to North America. Their adult body lengths (excluding tail) are known to vary approximately Normally. with mean u. = 36 millimeters (mm) and standard deviation 0 = 8 mm. Deer mice are found in diverse habitats and exhibit adaptations to their environment. A random sample of 14 deer mice in a rich forest habitat gives an average body length of 5 = 91.1 mm. Assume that the standard deviation 0- of all deer mice in this area is also 3 mm. Here is the output from the \"Fl-33 graphing calculator for a 95% condence interval based on these ndings: ZIntarval (86.909, 95.291) (a) What is the standard deviation of the sampling distribution of mean body lengths 5'? (Enter your answer rounded to four decimal places.) [b] What critical value was used to compute this 95% condence interval? (Enter your answer rounded to three decimal places.) 2*: (c) Which of the options are the step-by-step computations required to arrive at the interval provided by the graphing calculator? * + 1.645() =91.1 + (1.645) (2.1381) =91.1 + 3.517 mm. O 1 1.645( = 95.291 + (1.645) (8) = 95.291 + 13.16 mm. O 1 1.960( = 86.909 + (1.96) (8) = 86.909 + 15.68 mm. O x 1 1.960(- ()= 91.1 + (1.96)(2.1381) =91.1 + 4.191 mm. (d) Would a 90% confidence interval based on the data be larger or smaller? O The 90% confidence interval will be larger because the margin of error is smaller due to the smaller critical value. The 90% confidence interval will be larger because the margin of error is larger due to the larger critical value. O The 90% confidence interval will be smaller because the margin of error is smaller due to the smaller critical value. O The 90% confidence interval will be smaller because the margin of error is larger due to the larger critical value