The data below represents 40 samples taking from an assembly

The data below represents 40 samples taking from an assembly line that makes widgets. The customers only want to buy widgets that are 34.5 +- 3 mm.

Find the % defective of this process assuming the data follows a normal distribution with mean = sample process mean obtained and a deviation=sample process deviation obtained.

Find the % defective of this process from just the given data.

Create a histogram of the data with peaks ranging anywhere from 7 to 9.

Recommendations

X1

X2

X3

X4

X5

X6

X7

X8

X9

1

31.08374

35.669

35.35345

33.65292

33.98178

37.45832

34.48269

33.13399

36.08996

2

37.46899

35.46282

35.5877

36.12313

35.83815

32.13961

35.43835

35.70467

38.61359

3

37.735

32.10694

35.69216

34.90569

36.22805

39.20259

31.84397

36.84248

32.59359

4

30.77148

31.6781

33.22578

36.3241

33.30976

34.6476

36.9087

33.95705

33.80614

5

31.89682

36.18526

32.68002

36.1802

33.79708

34.78489

34.77676

28.90064

35.43781

6

34.25797

31.53706

34.04755

42.0427

37.54375

37.1164

33.68405

31.801

38.48031

7

37.38052

35.13436

39.24667

31.31113

37.35091

36.85677

34.65931

32.69277

39.78858

8

32.29378

34.72648

36.08645

36.24089

37.09823

33.45795

40.51511

33.81712

37.74781

9

31.49342

35.42491

33.16015

37.0638

37.41851

36.23166

32.51458

33.5102

32.78135

10

35.5101

36.24955

38.17491

34.97785

34.33229

36.23716

36.52248

35.1275

35.1704

11

36.65479

33.41702

36.74489

36.61113

36.81114

37.81676

33.34885

34.73764

31.87616

12

34.32994

34.33135

34.71596

34.46183

33.29645

37.99545

38.59794

38.78129

37.95235

13

36.13211

36.33347

32.62042

36.62468

34.91681

35.45727

38.19

36.79389

38.41283

14

32.47748

37.25973

30.41921

36.96377

35.38698

33.2141

35.79215

36.64019

33.53546

15

34.69996

35.65591

36.21214

32.54465

37.30788

35.64643

33.18272

37.45496

35.32785

16

34.7416

39.92473

38.11449

34.47828

33.55501

34.53285

36.61721

34.3917

34.4936

17

31.50735

35.20445

34.39695

35.43994

39.72643

35.14363

35.92657

34.64733

35.93812

18

34.77953

36.34049

34.77866

33.41985

36.73409

33.09403

39.62718

38.87666

33.53327

19

36.84612

34.69014

31.94396

32.53233

35.73805

36.77721

38.02231

31.00132

36.10918

20

37.63385

35.90485

34.25471

33.35522

33.242

31.36945

39.94987

31.50505

34.58975

21

38.32287

34.61822

37.26632

34.88996

34.48949

37.16607

33.87886

32.9619

36.70755

22

34.95497

33.26049

29.42006

33.78986

33.11338

36.38413

32.949

33.01174

31.64851

23

35.40947

36.25087

35.83111

32.86727

37.16872

39.29028

32.9853

33.5158

36.34615

24

32.98887

32.72028

37.49483

35.15706

35.47034

38.5291

34.18646

35.71513

35.99286

25

40.52536

36.06664

34.95775

32.92244

31.9727

32.74319

32.41698

33.75882

36.59139

26

34.59609

31.06465

33.75193

35.77343

32.53384

33.00013

34.47564

36.75664

34.86597

27

33.65781

34.50351

33.58826

41.83144

35.31054

36.69208

32.77244

33.20627

35.02187

28

32.53277

34.65942

35.52159

36.22886

35.05178

32.86841

35.6136

34.79315

30.88827

29

37.02577

33.03088

32.14972

39.13032

33.94403

33.95171

34.33647

34.59274

37.62521

30

35.54364

31.26975

33.226

31.97911

35.94731

30.94243

32.78534

36.93004

36.16711

31

32.43846

37.24083

33.09876

35.55251

34.80033

32.2171

33.3764

34.69829

36.05503

32

34.33712

34.36252

35.58179

39.20101

34.39872

35.76949

38.31214

33.58656

37.7835

33

33.32076

37.80344

34.24528

33.6067

35.89444

33.7851

37.38479

34.07854

38.98892

34

38.24219

34.37698

37.54435

35.7222

33.85896

33.11739

34.63257

37.14574

35.63858

35

37.48019

35.10588

35.8095

35.89737

35.13802

33.04888

36.40232

38.36104

37.21622

36

33.84414

34.27264

34.3991

36.78117

34.26403

31.97198

31.27722

35.14933

33.51778

37

33.46044

33.37498

33.88084

35.40053

35.76054

33.25707

32.22808

34.96106

36.03693

38

32.64028

35.16198

35.30923

34.17786

37.6596

35.36712

35.42534

35.28488

37.29228

39

32.76444

35.88662

33.88878

31.07241

36.1294

34.25418

32.30712

34.56793

32.55209

40

34.37319

32.84496

34.86397

35.36871

36.86046

33.50335

38.12522

35.92701

32.42381

	X1	X2	X3	X4	X5	X6	X7	X8	X9
1	31.08374	35.669	35.35345	33.65292	33.98178	37.45832	34.48269	33.13399	36.08996
2	37.46899	35.46282	35.5877	36.12313	35.83815	32.13961	35.43835	35.70467	38.61359
3	37.735	32.10694	35.69216	34.90569	36.22805	39.20259	31.84397	36.84248	32.59359
4	30.77148	31.6781	33.22578	36.3241	33.30976	34.6476	36.9087	33.95705	33.80614
5	31.89682	36.18526	32.68002	36.1802	33.79708	34.78489	34.77676	28.90064	35.43781
6	34.25797	31.53706	34.04755	42.0427	37.54375	37.1164	33.68405	31.801	38.48031
7	37.38052	35.13436	39.24667	31.31113	37.35091	36.85677	34.65931	32.69277	39.78858
8	32.29378	34.72648	36.08645	36.24089	37.09823	33.45795	40.51511	33.81712	37.74781
9	31.49342	35.42491	33.16015	37.0638	37.41851	36.23166	32.51458	33.5102	32.78135
10	35.5101	36.24955	38.17491	34.97785	34.33229	36.23716	36.52248	35.1275	35.1704
11	36.65479	33.41702	36.74489	36.61113	36.81114	37.81676	33.34885	34.73764	31.87616
12	34.32994	34.33135	34.71596	34.46183	33.29645	37.99545	38.59794	38.78129	37.95235
13	36.13211	36.33347	32.62042	36.62468	34.91681	35.45727	38.19	36.79389	38.41283
14	32.47748	37.25973	30.41921	36.96377	35.38698	33.2141	35.79215	36.64019	33.53546
15	34.69996	35.65591	36.21214	32.54465	37.30788	35.64643	33.18272	37.45496	35.32785
16	34.7416	39.92473	38.11449	34.47828	33.55501	34.53285	36.61721	34.3917	34.4936
17	31.50735	35.20445	34.39695	35.43994	39.72643	35.14363	35.92657	34.64733	35.93812
18	34.77953	36.34049	34.77866	33.41985	36.73409	33.09403	39.62718	38.87666	33.53327
19	36.84612	34.69014	31.94396	32.53233	35.73805	36.77721	38.02231	31.00132	36.10918
20	37.63385	35.90485	34.25471	33.35522	33.242	31.36945	39.94987	31.50505	34.58975
21	38.32287	34.61822	37.26632	34.88996	34.48949	37.16607	33.87886	32.9619	36.70755
22	34.95497	33.26049	29.42006	33.78986	33.11338	36.38413	32.949	33.01174	31.64851
23	35.40947	36.25087	35.83111	32.86727	37.16872	39.29028	32.9853	33.5158	36.34615
24	32.98887	32.72028	37.49483	35.15706	35.47034	38.5291	34.18646	35.71513	35.99286
25	40.52536	36.06664	34.95775	32.92244	31.9727	32.74319	32.41698	33.75882	36.59139
26	34.59609	31.06465	33.75193	35.77343	32.53384	33.00013	34.47564	36.75664	34.86597
27	33.65781	34.50351	33.58826	41.83144	35.31054	36.69208	32.77244	33.20627	35.02187
28	32.53277	34.65942	35.52159	36.22886	35.05178	32.86841	35.6136	34.79315	30.88827
29	37.02577	33.03088	32.14972	39.13032	33.94403	33.95171	34.33647	34.59274	37.62521
30	35.54364	31.26975	33.226	31.97911	35.94731	30.94243	32.78534	36.93004	36.16711
31	32.43846	37.24083	33.09876	35.55251	34.80033	32.2171	33.3764	34.69829	36.05503
32	34.33712	34.36252	35.58179	39.20101	34.39872	35.76949	38.31214	33.58656	37.7835
33	33.32076	37.80344	34.24528	33.6067	35.89444	33.7851	37.38479	34.07854	38.98892
34	38.24219	34.37698	37.54435	35.7222	33.85896	33.11739	34.63257	37.14574	35.63858
35	37.48019	35.10588	35.8095	35.89737	35.13802	33.04888	36.40232	38.36104	37.21622
36	33.84414	34.27264	34.3991	36.78117	34.26403	31.97198	31.27722	35.14933	33.51778
37	33.46044	33.37498	33.88084	35.40053	35.76054	33.25707	32.22808	34.96106	36.03693
38	32.64028	35.16198	35.30923	34.17786	37.6596	35.36712	35.42534	35.28488	37.29228
39	32.76444	35.88662	33.88878	31.07241	36.1294	34.25418	32.30712	34.56793	32.55209
40	34.37319	32.84496	34.86397	35.36871	36.86046	33.50335	38.12522	35.92701	32.42381

Solution

Take mean of all x1, to x6 and find the probability how they differ from 34.5 that will be your error

Probability deviating from themean