A cheese processing company wants to estimate the mean cholesterol content of allone-ounce servings of a type of cheese. The estimate must be within 0.72 milligram of the population mean.

(a) Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 3.04 milligrams.

(b) The sample mean is 30 milligrams. Using the minimum sample size with a 95% level ofconfidence, does it seem likely that the population mean could be within 3% of the samplemean? within 0.3% of the samplemean? Explain.

page 1:

z

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.00

3.4

0.0002

0.0003

0.0003

0.0003

0.0003

0.0003

0.0003

0.0003

0.0003

0.0003

3.3

0.0003

0.0004

0.0004

0.0004

0.0004

0.0004

0.0004

0.0005

0.0005

0.0005

3.2

0.0005

0.0005

0.0005

0.0006

0.0006

0.0006

0.0006

0.0006

0.0007

0.0007

3.1

0.0007

0.0007

0.0008

0.0008

0.0008

0.0008

0.0009

0.0009

0.0009

0.0010

3.0

0.0010

0.0010

0.0011

0.0011

0.0011

0.0012

0.0012

0.0013

0.0013

0.0013

2.9

0.0014

0.0014

0.0015

0.0015

0.0016

0.0016

0.0017

0.0018

0.0018

0.0019

2.8

0.0019

0.0020

0.0021

0.0021

0.0022

0.0023

0.0023

0.0024

0.0025

0.0026

2.7

0.0026

0.0027

0.0028

0.0029

0.0030

0.0031

0.0032

0.0033

0.0034

0.0035

2.6

0.0036

0.0037

0.0038

0.0039

0.0040

0.0041

0.0043

0.0044

0.0045

0.0047

2.5

0.0048

0.0049

0.0051

0.0052

0.0054

0.0055

0.0057

0.0059

0.0060

0.0062

2.4

0.0064

0.0066

0.0068

0.0069

0.0071

0.0073

0.0075

0.0078

0.0080

0.0082

2.3

0.0084

0.0087

0.0089

0.0091

0.0094

0.0096

0.0099

0.0102

0.0104

0.0107

2.2

0.0110

0.0113

0.0116

0.0119

0.0122

0.0125

0.0129

0.0132

0.0136

0.0139

2.1

0.0143

0.0146

0.0150

0.0154

0.0158

0.0162

0.0166

0.0170

0.0174

0.0179

2.0

0.0183

0.0188

0.0192

0.0197

0.0202

0.0207

0.0212

0.0217

0.0222

0.0228

1.9

0.0233

0.0239

0.0244

0.0250

0.0256

0.0262

0.0268

0.0274

0.0281

0.0287

1.8

0.0294

0.0301

0.0307

0.0314

0.0322

0.0329

0.0336

0.0344

0.0351

0.0359

1.7

0.0367

0.0375

0.0384

0.0392

0.0401

0.0409

0.0418

0.0427

0.0436

0.0446

1.6

0.0455

0.0465

0.0475

0.0485

0.0495

0.0505

0.0516

0.0526

0.0537

0.0548

1.5

0.0559

0.0571

0.0582

0.0594

0.0606

0.0618

0.0630

0.0643

0.0655

0.0668

1.4

0.0681

0.0694

0.0708

0.0721

0.0735

0.0749

0.0764

0.0778

0.0793

0.0808

1.3

0.0823

0.0838

0.0853

0.0869

0.0885

0.0901

0.0918

0.0934

0.0951

0.0968

1.2

0.0985

0.1003

0.1020

0.1038

0.1056

0.1075

0.1093

0.1112

0.1131

0.1151

1.1

0.1170

0.1190

0.1210

0.1230

0.1251

0.1271

0.1292

0.1314

0.1335

0.1357

1.0

0.1379

0.1401

0.1423

0.1446

0.1469

0.1492

0.1515

0.1539

0.1562

0.1587

0.9

0.1611

0.1635

0.1660

0.1685

0.1711

0.1736

0.1762

0.1788

0.1814

0.1841

0.8

0.1867

0.1894

0.1922

0.1949

0.1977

0.2005

0.2033

0.2061

0.2090

0.2119

0.7

0.2148

0.2177

0.2206

0.2236

0.2266

0.2296

0.2327

0.2358

0.2389

0.2420

0.6

0.2451

0.2483

0.2514

0.2546

0.2578

0.2611

0.2643

0.2676

0.2709

0.2743

0.5

0.2776

0.2810

0.2843

0.2877

0.2912

0.2946

0.2981

0.3015

0.3050

0.3085

0.4

0.3121

0.3156

0.3192

0.3228

0.3264

0.3300

0.3336

0.3372

0.3409

0.3446

0.3

0.3483

0.3520

0.3557

0.3594

0.3632

0.3669

0.3707

0.3745

0.3783

0.3821

0.2

0.3859

0.3897

0.3936

0.3974

0.4013

0.4052

0.4090

0.4129

0.4168

0.4207

0.1

0.4247

0.4286

0.4325

0.4364

0.4404

0.4443

0.4483

0.4522

0.4562

0.4602

0.0

0.4641

0.4681

0.4721

0.4761

0.4801

0.4840

0.4880

0.4920

0.4960

0.5000

z

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.00

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z

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.0

0.5000

0.5040

0.5080

0.5120

0.5160

0.5199

0.5239

0.5279

0.5319

0.5359

0.1

0.5398

0.5438

0.5478

0.5517

0.5557

0.5596

0.5636

0.5675

0.5714

0.5753

0.2

0.5793

0.5832

0.5871

0.5910

0.5948

0.5987

0.6026

0.6064

0.6103

0.6141

0.3

0.6179

0.6217

0.6255

0.6293

0.6331

0.6368

0.6406

0.6443

0.6480

0.6517

0.4

0.6554

0.6591

0.6628

0.6664

0.6700

0.6736

0.6772

0.6808

0.6844

0.6879

0.5

0.6915

0.6950

0.6985

0.7019

0.7054

0.7088

0.7123

0.7157

0.7190

0.7224

0.6

0.7257

0.7291

0.7324

0.7357

0.7389

0.7422

0.7454

0.7486

0.7517

0.7549

0.7

0.7580

0.7611

0.7642

0.7673

0.7704

0.7734

0.7764

0.7794

0.7823

0.7852

0.8

0.7881

0.7910

0.7939

0.7967

0.7995

0.8023

0.8051

0.8078

0.8106

0.8133

0.9

0.8159

0.8186

0.8212

0.8238

0.8264

0.8289

0.8315

0.8340

0.8365

0.8389

1.0

0.8413

0.8438

0.8461

0.8485

0.8508

0.8531

0.8554

0.8577

0.8599

0.8621

1.1

0.8643

0.8665

0.8686

0.8708

0.8729

0.8749

0.8770

0.8790

0.8810

0.8830

1.2

0.8849

0.8869

0.8888

0.8907

0.8925

0.8944

0.8962

0.8980

0.8997

0.9015

1.3

0.9032

0.9049

0.9066

0.9082

0.9099

0.9115

0.9131

0.9147

0.9162

0.9177

1.4

0.9192

0.9207

0.9222

0.9236

0.9251

0.9265

0.9279

0.9292

0.9306

0.9319

1.5

0.9332

0.9345

0.9357

0.9370

0.9382

0.9394

0.9406

0.9418

0.9429

0.9441

1.6

0.9452

0.9463

0.9474

0.9484

0.9495

0.9505

0.9515

0.9525

0.9535

0.9545

1.7

0.9554

0.9564

0.9573

0.9582

0.9591

0.9599

0.9608

0.9616

0.9625

0.9633

1.8

0.9641

0.9649

0.9656

0.9664

0.9671

0.9678

0.9686

0.9693

0.9699

0.9706

1.9

0.9713

0.9719

0.9726

0.9732

0.9738

0.9744

0.9750

0.9756

0.9761

0.9767

2.0

0.9772

0.9778

0.9783

0.9788

0.9793

0.9798

0.9803

0.9808

0.9812

0.9817

2.1

0.9821

0.9826

0.9830

0.9834

0.9838

0.9842

0.9846

0.9850

0.9854

0.9857

2.2

0.9861

0.9864

0.9868

0.9871

0.9875

0.9878

0.9881

0.9884

0.9887

0.9890

2.3

0.9893

0.9896

0.9898

0.9901

0.9904

0.9906

0.9909

0.9911

0.9913

0.9916

2.4

0.9918

0.9920

0.9922

0.9925

0.9927

0.9929

0.9931

0.9932

0.9934

0.9936

2.5

0.9938

0.9940

0.9941

0.9943

0.9945

0.9946

0.9948

0.9949

0.9951

0.9952

2.6

0.9953

0.9955

0.9956

0.9957

0.9959

0.9960

0.9961

0.9962

0.9963

0.9964

2.7

0.9965

0.9966

0.9967

0.9968

0.9969

0.9970

0.9971

0.9972

0.9973

0.9974

2.8

0.9974

0.9975

0.9976

0.9977

0.9977

0.9978

0.9979

0.9979

0.9980

0.9981

2.9

0.9981

0.9982

0.9982

0.9983

0.9984

0.9984

0.9985

0.9985

0.9986

0.9986

3.0

0.9987

0.9987

0.9987

0.9988

0.9988

0.9989

0.9989

0.9989

0.9990

0.9990

3.1

0.9990

0.9991

0.9991

0.9991

0.9992

0.9992

0.9992

0.9992

0.9993

0.9993

3.2

0.9993

0.9993

0.9994

0.9994

0.9994

0.9994

0.9994

0.9995

0.9995

0.9995

3.3

0.9995

0.9995

0.9995

0.9996

0.9996

0.9996

0.9996

0.9996

0.9996

0.9997

3.4

0.9997

0.9997

0.9997

0.9997

0.9997

0.9997

0.9997

0.9997

0.9997

0.9998

z

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

(a) The minimum sample size required to construct a 95% confidence interval is

nothing

servings.

(Round up to the nearest wholenumber.)

(b) The 95% confidence interval is (

nothing

,

nothing

). It

does

does not

seem likely that the population mean could be within 3% of the sample mean because 3% off from the sample mean would fall

inside

outside

the confidence interval. It

does not

does

seem likely that the population mean could be within 0.3% of the sample mean because 0.3% off from the sample mean would fall

inside

outside

the confidence interval.