4.3

1. discrete

2. continuous

3. continuous

4. discrete

5. continuous

6. continuous

4.5

1. continuous

2. discrete

3. discrete

4. discrete

5. discrete

6. continuous

4.7 0, 1, 2, 3, …; discrete

4.9 continuous; discrete

4.11 gender; IQ score

4.13 allergy to penicillin; blood pressure

4.17 table, graph, formula

4.19 no

4.21

1. .25

2. .35

3. .8

4.23

1. .7

2. .3

3. 1

4. .2

5. .8

4.25

1. 3.8

2. 10.56

3. 3.25

4. no

5. yes

4.27

1. ${\mu }_x=1,{\mu }_y=1$

2. distribution of x

3. ${\mu }_x=1,{\sigma }^2=.6;{\mu }_y=1,{\sigma }^2=.2$

4.29

1. 0, 2, 3, 4

2. $P(0)=.330,$ $P(2)=.547,P(3)=.047,$ $P(4)=.075$

3. 1.54

4.31

1. b. .14

2. c. 4.66; 19.86

3. d.

   $(-4.26,13.57)$

4.33

1. BB, BG, GB, GG

2. ${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$, ${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$, $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$, ${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$,

3. $P(0)=.25$, $P(1)=.5$, $P(2)=.25$

4. $P(0)=.222$, $P(1)=.513$, $P(2)=.265$

4.35

1. $P(\text{any letter)}=1/26$

2. no

4.37

1. .23

2. .081

3. .77

4.39

1. $P(6)=.282$, $P(7)=.065$, $P(8)=.339$, $P(9)=.032$, $P(10)=.008$, $P(11)=.274$

2. .274

4.41

1. MC, MS, MB, MO, ML, CS, CB, CO, CL, SB, SO, SL, BO, BL, OL

2. equally likely, with $p=1/15$

3. $P(0)=6/15,P(1)=8/15,P(2)=1/15$

4. .667

4.43 $-\$0.263$

4.45

1. voters 1, 2, 3, 4, 7, 8, 10: 2; voter 5: 0; voter 6: 1, voter 9: 3

2. $P(0)=.10$, $P(1)=.10$, $P(2)=.70$, $P(3)=.10$

3. .10

4. no

4.47

1. 0, 1, 2

2. $P(0)=.625$, $P(1)=.250,P(2)=.125$

4.49 $\left(\begin{array}{l}7\\ x\end{array}\right){(.2)}^x{(.8)}^{7-x}$

4.51

1. 15

2. 10

3. 1

4. 1

5. 4

4.53

1. .4096

2. .3456

3. .027

4. .0081

5. .3456

6. .027

4.55

1. 0

2. .998

3. .137

4.57

1. $p=.5$

2. $p<.5$

3. $p>.5$

4.59

1. a. believe finding/picking up penny is good luck

2. c. .33

3. d. .9134

4. e. .0000022

5. f. .6917

4.61

1. b. 40

2. c. 24

3. d. (30.2, 49.8)

4.63

1. .659

2. .237

4.65

1. a. .375

2. b. .5

4.67

1. .791

2. .056

3. rare event if $p=.1$

4.69

1. .1

2. .7

3. .4783

4. .0078

5. yes

4.71

1. b. $\mu =2.4,$ $\sigma =1.47$

2. c. $p=.9,q=.1,n=24,\mu =21.6,\sigma =1.47$

4.73 symmetric, bell-shaped

4.75 standard normal

4.77

1. 0

2. .8413

3. .8413

4. .1587

5. .6826

6. .9544

7. .6934

8. .6378

4.79

1. 1

2. $-1$

3. 0

4. $-2.5$

5. 3

4.81

1. 1.645

2. 1.96

3. $-1.96$

4. 1.28

5. 1.28

4.83

1. 30

2. 14.32

3. 40.24

4. 16.84

5. 19.76

6. 36.72

7. 48.64

4.85

1. $-.25$

2. .44

3. .0122

4.87

1. .8185

2. .9082

3. 2.55

4.89

1. .4207

2. .000337

4.91.0548

4.93

1. .9414

2. .9996

4.95

1. no; $P(x\le 9)=.8413$

2. no; $P(x\le 2)=.0139$

4.97.7019

4.99

1. $z_L=-.675,z_U=.675$

2. $-2.68,2.68$

3. $-4.69,4.69$

4. .0074, 0

4.101

1. (62.26, 65.74); (61.01, 66.99); (59.72, 68.28); (58.90, 69.10); (57.30, 70.70)

4.105

1. .68

2. .95

3. .997

4.107 plot c

4.109

1. not normal (skewed right)

2. $Q_L=37.5,Q_U=152.8,s=95.8$

3. $\text{IQR/s}=1.204$

4.111 no

4.113 no; $\text{IQR/s}=.82$

4.115

1. histogram too peaked

2. more than 95%

4.117 both

4.119 both distributions approx. normal

4.121 no

4.123 TT approx. normal

4.127

1. yes

2. $\mu =10,{\sigma }^2=6$

3. .726

4. .7291

4.129

1. .345; .3446

2. .115; .1151

3. .924; .9224

4.131

1. .1788

2. .5236

3. .6950

4.133

1. 350

2. 227.5

3. .0455

4. no, $P(x\ge 390)=.0044$

4.135

1. 4.73

2. 14.75

3. $-8.10$

4. $\approx 0$

4.137 $\approx 0$

4.139

1. 1

2. .9772

4.141 event not likely to occur; probability less than .9

4.145

1. c. 1/16

4.147

1. c. .05

2. d. no

4.149

1. 

   Alternate View

   M	1	1.5	2	2.5	3	3.5	4	4.5	5
   P(M)	.04	.12	.17	.20	.20	.14	.08	.04	.01

4.157

1. $\mu =100,\sigma =5$

2. $\mu =100,\sigma =2$

3. $\mu =100,\sigma =1$

4. $\mu =100,\sigma =1.414$

5. $\mu =100,\sigma =.447$

6. $\mu =100,\sigma =.316$

4.159

1. a. $\mu =2.9,{\sigma }^2=3.29$, $\sigma =1.814$

2. c. ${\mu }_{\bar{x}}=2.9,{\sigma }_{\bar{x}}=1.283$

4.161

1. ${\mu }_{\bar{x}}=30,{\sigma }_{\bar{x}}=1.6$

2. approx. normal

3. .8944

4. .0228

5. .1303

6. .9699

4.163

1. 353

2. 20

3. approx. normal

4. d. $\approx 0$

4.165

1. ${\mu }_{\bar{x}}=320,{\sigma }_{\bar{x}}=10,$ approx. normal

2. .1359

3. 0

4.167

1. 1,800

2. 18,000

3. approx. normal

4. .5468

5. .0681

4.169 No, $P(\bar{x}<103)=.0107$

4.171

1. 10; .0002

2. Central Limit Theorem

3. .0170

4.173

1. .0034

2. $\mu >6$

4.175 handrubbing: $P(\bar{x}<30)=.2743;$ handwashing: $P(\bar{x}<30)=.0047;$ sample used handrubbing

4.177

1. yes

2. no

3. no

4. yes

4.179 false

4.181 true

4.183

1. .192

2. .228

3. .772

4. .987

5. .960

6. 14; 4.2; 2.05

7. .975

4.185

1. .5

2. .0606

3. .0985

4. .8436

4.185

1. 40

2. 54.22

3. 23.38

4. 52

5. 32.32

6. 34.96

 4.187

1. .087

2. 3.0002

4.189

1. b. $n=20,p=.8$

2. c. .174

3. d. .804

4. e. 16

4.191

1. 1

2. .24

3. .39

4. 1.8

5. .9899

6. .96

4.193

1. .001

2. .322

3. .994

4.195 83.15%

4.197

1. .8413

2. .7528

4.199

1. 106

2. 2.73

3. approx. normal

4. $-2.20$

5. .0136

4.201

1. b. .0524

4.203.642

4.205.049

4.207

1. .0735

2. .3651

3. 7.29

4.209 no

4.211

1. No, prob. $\approx 0$

2. likely that $\mu >4.59$

4.213

1. ${\mu }_{\bar{x}}=.53,{\sigma }_{\bar{x}}=.0273$, approx. normal

2. .0336

3. after

4.215 $\approx 292$

4.217

1. .0031

2. more; less

3. less; more

4.219

1. .05, .20, .50, .20, .05

2. z-scores

3. identical