A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 99% confident that the sample mean is correct to within $60 of the population mean annual family medical expenses. A previous study indicates that the standard deviation is approximately $397.

a. How large a sample isnecessary?

b. If management wants to be correct to within $20, how many employees need to beselected?

Click here to view page 1 of the cumulative standardized normal distribution table.1

Click here to view page 2 of the cumulative standardized normal distribution table.2

a. How large a sample isnecessary?

n=

(Round up to the nearestinteger.)

b. If management wants to be correct to within $20, how many employees need to beselected?

n=

(Round up to the nearestinteger.)

Cumulative Probabilities

Z

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

6.0

0.000000001

5.5

0.000000019

5.0

0.000000287

4.5

0.000003398

4.0

0.000031671

3.9

0.00005

0.00005

0.00004

0.00004

0.00004

0.00004

0.00004

0.00003

0.00003

0.00003

3.8

0.00007

0.00007

0.00007

0.00006

0.00006

0.00006

0.00006

0.00005

0.00005

0.00005

3.7

0.00011

0.00010

0.00010

0.00010

0.00009

0.00009

0.00008

0.00008

0.00008

0.00008

3.6

0.00016

0.00015

0.00015

0.00014

0.00014

0.00013

0.00013

0.00012

0.00012

0.00011

3.5

0.00023

0.00022

0.00022

0.00021

0.00020

0.00019

0.00019

0.00018

0.00017

0.00017

3.4

0.00034

0.00032

0.00031

0.00030

0.00029

0.00028

0.00027

0.00026

0.00025

0.00024

3.3

0.00048

0.00047

0.00045

0.00043

0.00042

0.00040

0.00039

0.00038

0.00036

0.00035

3.2

0.00069

0.00066

0.00064

0.00062

0.00060

0.00058

0.00056

0.00054

0.00052

0.00050

3.1

0.00097

0.00094

0.00090

0.00087

0.00084

0.00082

0.00079

0.00076

0.00074

0.00071

3.0

0.00135

0.00131

0.00126

0.00122

0.00118

0.00114

0.00111

0.00107

0.00103

0.00100

2.9

0.0019

0.0018

0.0018

0.0017

0.0016

0.0016

0.0015

0.0015

0.0014

0.0014

2.8

0.0026

0.0025

0.0024

0.0023

0.0023

0.0022

0.0021

0.0021

0.0020

0.0019

2.7

0.0035

0.0034

0.0033

0.0032

0.0031

0.0030

0.0029

0.0028

0.0027

0.0026

2.6

0.0047

0.0045

0.0044

0.0043

0.0041

0.0040

0.0039

0.0038

0.0037

0.0036

2.5

0.0062

0.0060

0.0059

0.0057

0.0055

0.0054

0.0052

0.0051

0.0049

0.0048

2.4

0.0082

0.0080

0.0078

0.0075

0.0073

0.0071

0.0069

0.0068

0.0066

0.0064

2.3

0.0107

0.0104

0.0102

0.0099

0.0096

0.0094

0.0091

0.0089

0.0087

0.0084

2.2

0.0139

0.0136

0.0132

0.0129

0.0125

0.0122

0.0119

0.0116

0.0113

0.0110

2.1

0.0179

0.0174

0.0170

0.0166

0.0162

0.0158

0.0154

0.0150

0.0146

0.0143

2.0

0.0228

0.0222

0.0217

0.0212

0.0207

0.0202

0.0197

0.0192

0.0188

0.0183

1.9

0.0287

0.0281

0.0274

0.0268

0.0262

0.0256

0.0250

0.0244

0.0239

0.0233

1.8

0.0359

0.0351

0.0344

0.0336

0.0329

0.0322

0.0314

0.0307

0.0301

0.0294

1.7

0.0446

0.0436

0.0427

0.0418

0.0409

0.0401

0.0392

0.0384

0.0375

0.0367

1.6

0.0548

0.0537

0.0526

0.0516

0.0505

0.0495

0.0485

0.0475

0.0465

0.0455

1.5

0.0668

0.0655

0.0643

0.0630

0.0618

0.0606

0.0594

0.0582

0.0571

0.0559

1.4

0.0808

0.0793

0.0778

0.0764

0.0749

0.0735

0.0721

0.0708

0.0694

0.0681

1.3

0.0968

0.0951

0.0934

0.0918

0.0901

0.0885

0.0869

0.0853

0.0838

0.0823

1.2

0.1151

0.1131

0.1112

0.1093

0.1075

0.1056

0.1038

0.1020

0.1003

0.0985

1.1

0.1357

0.1335

0.1314

0.1292

0.1271

0.1251

0.1230

0.1210

0.1190

0.1170

1.0

0.1587

0.1562

0.1539

0.1515

0.1492

0.1469

0.1446

0.1423

0.1401

0.1379

0.9

0.1841

0.1814

0.1788

0.1762

0.1736

0.1711

0.1685

0.1660

0.1635

0.1611

0.8

0.2119

0.2090

0.2061

0.2033

0.2005

0.1977

0.1949

0.1922

0.1894

0.1867

0.7

0.2420

0.2389

0.2358

0.2327

0.2296

0.2266

0.2236

0.2206

0.2177

0.2148

0.6

0.2743

0.2709

0.2676

0.2643

0.2611

0.2578

0.2546

0.2514

0.2483

0.2451

0.5

0.3085

0.3050

0.3015

0.2981

0.2946

0.2912

0.2877

0.2843

0.2810

0.2776

0.4

0.3446

0.3409

0.3372

0.3336

0.3300

0.3264

0.3228

0.3192

0.3156

0.3121

0.3

0.3821

0.3783

0.3745

0.3707

0.3669

0.3632

0.3594

0.3557

0.3520

0.3483

0.2

0.4207

0.4168

0.4129

0.4090

0.4052

0.4013

0.3974

0.3936

0.3897

0.3859

0.1

0.4602

0.4562

0.4522

0.4483

0.4443

0.4404

0.4364

0.4325

0.4286

0.4247

0.0

0.5000

0.4960

0.4920

0.4880

0.4840

0.4801

0.4761

0.4721

0.4681

0.4641

Cumulative Probabilities

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

0.99865

0.99869

0.99874

0.99878

0.99882

0.99886

0.99889

0.99893

0.99897

0.99900

3.1

0.99903

0.99906

0.99910

0.99913

0.99916

0.99918

0.99921

0.99924

0.99926

0.99929

3.2

0.99931

0.99934

0.99936

0.99938

0.99940

0.99942

0.99944

0.99946

0.99948

0.99950

3.3

0.99952

0.99953

0.99955

0.99957

0.99958

0.99960

0.99961

0.99962

0.99964

0.99965

3.4

0.99966

0.99968

0.99969

0.99970

0.99971

0.99972

0.99973

0.99974

0.99975

0.99976

3.5

0.99977

0.99978

0.99978

0.99979

0.99980

0.99981

0.99981

0.99982

0.99983

0.99983

3.6

0.99984

0.99985

0.99985

0.99986

0.99986

0.99987

0.99987

0.99988

0.99988

0.99989

3.7

0.99989

0.99990

0.99990

0.99990

0.99991

0.99991

0.99992

0.99992

0.99992

0.99992

3.8

0.99993

0.99993

0.99993

0.99994

0.99994

0.99994

0.99994

0.99995

0.99995

0.99995

3.9

0.99995

0.99995

0.99996

0.99996

0.99996

0.99996

0.99996

0.99996

0.99997

0.99997

4.0

0.999968329

4.5

0.999996602

5.0

0.999999713

5.5

0.999999981

6.0

0.999999999