Question

use the given data values (a sample of female arm circumferences in centimeters) to identify the corresponding z scores that are used for a normal quantile plot, then identify the coordinates of each point in the normal quantile plot. construct the normal quantile plot, then determine whether the data appear to be from a population with a normal distribution. 32.1, 45.0, 39.1, 40.7, 33.8 list the z scores for the normal quantile plot. -1.28, -0.52, 0, 0.52, 1.28 (round to two decimal places as needed. use ascending order.) identify the coordinates of each point in the normal quantile plot. use ordered pairs of the form (x,y), where x is the sorted arm circumferences, and y is the corresponding z score. (type ordered pairs. round to two decimal places as needed. use ascending order.)

Explanation:

Step1: Sort the data

Sort the sample of female arm circumferences: \(32.1\), \(33.8\), \(39.1\), \(40.7\), \(45.0\)

Step2: Match with z - scores

The given z - scores in ascending order are \(-1.28\), \(-0.52\), \(0\), \(0.52\), \(1.28\)

Step3: Form ordered pairs

Form ordered pairs \((x,y)\) where \(x\) is the sorted arm circumference and \(y\) is the corresponding z - score:
For \(x = 32.1\) and \(y=-1.28\), the ordered pair is \((32.1,-1.28)\)
For \(x = 33.8\) and \(y = - 0.52\), the ordered pair is \((33.8,-0.52)\)
For \(x = 39.1\) and \(y = 0\), the ordered pair is \((39.1,0)\)
For \(x = 40.7\) and \(y = 0.52\), the ordered pair is \((40.7,0.52)\)
For \(x = 45.0\) and \(y = 1.28\), the ordered pair is \((45.0,1.28)\)

Answer:

\((32.1,-1.28)\), \((33.8,-0.52)\), \((39.1,0)\), \((40.7,0.52)\), \((45.0,1.28)\)