Question

A random sample of 16 undergraduate students receiving student loans was​obtained, and the amounts of their loans for the school year were recorded. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed. 6,200 6,700 1,200 2,000 2,300 8,400 7,700 5,500 6,300 4,700 3,000 3,900 1,200 2,800 2,700 7,300

Using the correlation coefficient of the normal probability​ plot, is it reasonable to conclude that the population is normally​ distributed? Select the correct choice below and fill in the answer boxes within your choice.

A. No. The correlation between the expected​ z-scores and the observed​ data, _____ does not exceed the critical ​value, _______.​Therefore, it is not reasonable to conclude that the data come from a normal population.

B. Yes. The correlation between the expected​ z-scores and the observed​ data, _______ exceeds the critical​ value, ______. ​Therefore, it is reasonable to conclude that the data come from a normal population.

C. Yes. The correlation between the expected​ z-scores and the observed​ data, _______ exceeds the critical value _____. ​Therefore, it is not reasonable to conclude that the data come from a normal population.

D. No. The correlation between the expected​ z-scores and the observed​ data, _______ does not exceed the critical​value, ______. ​Therefore, it is reasonable to conclude that the data come from a normal population.

Answer 1

Rank,i	Proportion = i/(n+1)	Z score	Data
1	0.0588	-1.5647	1200
2	0.1176	-1.1868	1200
3	0.1765	-0.9289	2000
4	0.2353	-0.7215	2300
5	0.2941	-0.5414	2700
6	0.3529	-0.3774	2800
7	0.4118	-0.2230	3000
8	0.4706	-0.0738	3900
9	0.5294	0.0738	4700
10	0.5882	0.2230	5500
11	0.6471	0.3774	6200
12	0.7059	0.5414	6300
13	0.7647	0.7215	6700
14	0.8235	0.9289	7300
15	0.8824	1.1868	7700
16	0.9412	1.5647	8400

correlation between z-score and observed data=                   0.980
                  
critical correlation value for n=16 is 0.941                  

answer is

yes, the correlation between expected z score and observed data ,   0.980   excced the critical value 0.941,              
therefore, it is reasonable to conclude that data come from a normal population.