Draw a normal probability plot

Reference no: EM132403059

Questions -

Q1. Use the accompanying data table to (a) draw a normal probability plot, (b) determine the linear correlation between the observed values and the expected z-scores, (c) determine the critical value in the table of critical values of the correlation coefficient to assess the normality of the data.

Data Table

Index, i	Observed Value	f_i	Expected z-score
1	37	0.08	-1.41
2	38	0.20	-0.84
3	42	0.32	-0.47
4	45	0.44	-0.15
5	54	0.56	0.15
6	57	0.68	0.47
7	59	0.80	0.84
8	62	0.92	1.41

Critical Values of the Correlation Coefficient

Sample Size, n	Critical Value
5	0.880
6	0.888
7	0.898
8	0.906
9	0.912
10	0.918
11	0.923
12	0.928
13	0.932
14	0.935
15	0.939
16	0.941
17	0.944
18	0.946
19	0.949
20	0.951
21	0.952
22	0.954
23	0.956
24	0.957
25	0.959
30	0.960

Q2. Use the accompanying data table to (a) draw a normal probability plot, (b) determine the linear correlation between the observed values and the expected z-scores, (c) determine the critical value in the table of critical values of the correlation coefficient to assess the normality of the data.

Data Table

Index, i	Observed Value	f_i	Expected z-score
1	35	0.08	-1.41
2	38	0.20	-0.84
3	39	0.32	-0.47
4	46	0.44	-0.15
5	48	0.56	0.15
6	59	0.68	0.47
7	61	0.80	0.84
8	651	0.92	1.41

Q3. In an advertising campaign, a snack company claimed that every 18-ounce bag of its cookies contained at least 1000 chocolate chips. Two statisticians attempted to verify the claim. The accompanying data represent the number of chips in an 18-ounce bag of the company's cookies based on their study. Complete parts (a) through (e).

Chocolate Chip Data Table

1086	1156	1216	1270	1341
1101	1171	1216	1274	1358
1105	1185	1216	1283	1360
1117	1186	1226	1293	1376
1131	1196	1236	1295	1402
1137	1205	1242	1299	1420
1138	1211	1245	1302	1443
1140	1215	1259	1326	1515

(a) Draw a normal probability plot to determine if the data could have come from a normal distribution.

(b) Determine the mean and standard deviation of the sample data.

(c) Using the sample mean and sample standard deviation obtained in part (b) as estimates for the population mean and population standard deviation, respectively, draw a graph of a normal model for the distribution of chips in a bag of cookies.

(d) Using the normal model from part (c), find the probability that an 18-ounce bag of chips selected at random contains at least 1000 chips.

(e) Using the normal model from part (c), find the probability that an 18-ounce bag of chips selected at random contains between 1100 and 1400 chips.

Attachment:- Standard Normal Distribution Tables.rar

Reference no: EM132403059

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