Question

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 values z Subscript Upper L and z Subscript Upper U​, the lower and upper values of the standard normal random variable z​ respectively, for the lower and upper quartiles Upper Q Subscript Upper L and Upper Q Subscript Upper U of the probability distribution. z Subscript Upper Lequals nothing z Subscript Upper Uequals nothing ​(Round to two decimal places as​ needed.) b. Calculate the values z Subscript Upper L and z 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 Lequals nothing z Subscript Upper Uequals nothing ​(Round to two decimal places as​ needed.) c. Calculate the values z Subscript Upper L and z 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 Lequals nothing z Subscript Upper Uequals nothing ​(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 is nothing. The probability that an observation lies beyond the outer fences is nothing. ​(Round to three decimal places as​ needed.) e. Do these values help 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 ▼ relatively unlikely relatively likely extremely likely extremely unlikely that an observation lies beyond the inner​ fences, and ▼ relatively likely relatively unlikely extremely likely extremely unlikely that an observation lies beyond the outer fences.

Answer 1