What relationship exists between the standard normal distribution and the? box-plot methodology for describing distributions of data by means of? quartiles? the answer depends on the true underlying probability distribution of the data. assume for the remainder of this exercise that the distribution is normal. complete parts a through e below. a. calculate the valuesz subscript upper landz subscript upper u? ,the lower and upper values of the standard normal random variable z? respectively, for the lower and upper quartilesupper q subscript upper landupper q subscript upper uof the probability distribution. z subscript upper lequalsnothingz subscript upper uequalsnothing? (round to two decimal places as? needed.)b. calculate the valuesz subscript upper landz subscript upper u? ,the lower and upper values of the standard normal random variable z? respectively, for the inner fences of the box plot for a normal probability distribution. z subscript upper lequalsnothingz subscript upper uequalsnothing? (round to two decimal places as? needed.)c. calculate the valuesz subscript upper landz subscript upper u? ,the lower and upper values of the standard normal random variable z? respectively, for the outer fences of the box plot for a normal probability distribution. z subscript upper lequalsnothingz subscript upper uequalsnothing? (round to two decimal places as? needed.)d. what is the probability that an observation lies beyond the inner fences of a normal probability? distribution? the outer? fences? the probability that an observation lies beyond the inner fences isnothing. the probability that an observation lies beyond the outer fences to three decimal places as? needed.)e. do these values to explain why the inner and outer fences of a box plot are used to detect outliers in a? distribution? explain.? no, yes, because it is? extremely likelyrelatively unlikelyextremely unlikelyrelatively likelythat an observation lies beyond the inner? fences, and? extremely likelyrelatively unlikelyrelatively likelyextremely unlikelythat an observation lies beyond the outer fences. expert answer