Question

A sample of human brain volumes (cm3​) is given below. Use the given data values 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.

1055

1032

1079

1086

967

1086

1054

1445

(1) List the z scores for the normal quantile plot.

(2) Identify the coordinates of each point in the normal quantile plot. Use ordered pairs for the form​ (x,y), where x is the sorted human brain volumes in ascending​ order, and y is the corresponding z score.

(3) Do the data appear to come from a normally distributed​ population?

A.

​No, because the points in the normal quantile plot do not lie reasonably close to a straight line or show a systematic pattern that is a straight line pattern.

B.

​No, but the points in the normal quantile plot lie reasonably close to a straight line and show some systematic pattern that is a straight line pattern.

C.

​Yes, but the points in the normal quantile plot do not lie reasonably close to a straight line or show a systematic pattern that is a straight line pattern.

D.

​Yes, because the pattern of the points in the normal quantile plot is reasonably close to a straight line.

Answer 1

z scores for the normal quantile plot is obtained using following formula.

Sorted X	967	1032	1045	1054	1055	1079	1086	1086
Z score	-2.13	-0.47	-0.14	0.09	0.12	0.73	0.91	0.91

Normal quantile plot:

​Yes, because the pattern of the points in the normal quantile plot is reasonably close to a straight line.