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Solution Manual of Statistics for Managers Using Microsoft Excel Global Edition 8th Edition by David M

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  • ISBN-10 ‏ : ‎ 9332585741
  • ISBN-13 ‏ : ‎ 978-9332585744

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Solution Manual of Statistics for Managers Using Microsoft Excel Global Edition 8th Edition by David M

CHAPTER 6

6.1 (a) P(Z < 1.47) = 0.9292
(b) P(Z > 1.74) = 1 – 0.9591 = 0.0409
(c) P(1.37 < Z < 1.75) = 0.9599 – 0.9147 = 0.0452
(d) P(Z < 1.67) + P(Z > 1.78) = 0.9525 + (1 – 0.9625) = 0.99

6.2 PHStat output:
Normal Probabilities

Common Data
Mean 0
Standard Deviation 1
Probability for a Range
Probability for X <= From X Value 1.57
X Value -1.57 To X Value 1.84
Z Value -1.57 Z Value for 1.57 1.57
P(X<=-1.57) 0.0582076 Z Value for 1.84 1.84
P(X<=1.57) 0.9418
Probability for X > P(X<=1.84) 0.9671
X Value 1.84 P(1.57<=X<=1.84) 0.0253
Z Value 1.84
P(X>1.84) 0.0329 Find X and Z Given Cum. Pctage.
Cumulative Percentage 84.13%
Probability for X<-1.57 or X >1.84 Z Value 0.999815
P(X<-1.57 or X >1.84) 0.0911 X Value 0.999815
(a) P(– 1.57 < Z < 1.84) = 0.9671 – 0.0582 = 0.9089
(b) P(Z < – 1.57) + P(Z > 1.84) = 0.0582 + 0.0329 = 0.0911
(c) If P(Z > A) = 0.025, P(Z < A) = 0.975. A = + 1.96.
(d) If P(–A < Z < A) = 0.6826, P(Z < A) = 0.8413. So 68.26% of the area is captured between –A = – 1.00 and A = + 1.00.

6.3 (a) Partial PHStat output:
Normal Probabilities

Common Data
Mean 0
Standard Deviation 1
Probability for a Range
Probability for X <= From X Value 1.57
X Value 1.08 To X Value 1.84
Z Value 1.08 Z Value for 1.57 1.57
P(X<=1.08) 0.8599289 Z Value for 1.84 1.84
P(X<=1.57) 0.9418
Probability for X > P(X<=1.84) 0.9671
X Value -0.21 P(1.57<=X<=1.84) 0.0253
Z Value -0.21
P(X>-0.21) 0.5832 Find X and Z Given Cum. Pctage.
Cumulative Percentage 84.13%
Probability for X<1.08 or X >-0.21 Z Value 0.999815
P(X<1.08 or X >-0.21) 1.4431 X Value 0.999815
P(Z < 1.08) = 0.8599
(b) P(Z > – 0.21) = 1.0 – 0.4168 = 0.5832
(c) Partial PHStat output:
Probability for X<-0.21 or X >0
P(X<-0.21 or X >0) 0.9168
P(Z < – 0.21) + P(Z > 0) = 0.4168 + 0.5 = 0.9168
(d) Partial PHStat output:
Probability for X<-0.21 or X >1.08
P(X<-0.21 or X >1.08) 0.5569
P(Z < – 0.21) + P(Z > 1.08) = 0.4168 + (1 – 0.8599) = 0.5569

6.4 PHStat output:
Normal Probabilities

Common Data
Mean 0
Standard Deviation 1
Probability for a Range
Probability for X <= From X Value -1.96
X Value -0.21 To X Value -0.21
Z Value -0.21 Z Value for -1.96 -1.96
P(X<=-0.21) 0.4168338 Z Value for -0.21 -0.21
P(X<=-1.96) 0.0250
Probability for X > P(X<=-0.21) 0.4168
X Value 1.08 P(-1.96<=X<=-0.21) 0.3918
Z Value 1.08
P(X>1.08) 0.1401 Find X and Z Given Cum. Pctage.
Cumulative Percentage 84.13%
Probability for X<-0.21 or X >1.08 Z Value 0.999815
P(X<-0.21 or X >1.08) 0.5569 X Value 0.999815
(a) P(Z > 1.08) = 1 – 0.8599 = 0.1401
(b) P(Z < – 0.21) = 0.4168
(c) P(– 1.96 < Z < – 0.21) = 0.4168 – 0.0250 = 0.3918
(d) P(Z > A) = 0.1587, P(Z < A) = 0.8413. A = + 1.00.

6.5 (a)
P(X > 65) = P(Z > –2.50) = 1 – P(Z < –2.50) = 1 – 0.0062 = 0.9938

(b)
P(X < 60) = P(Z < – 3.00) = 0.00135

(c)
P(X < 70) = P(Z < –2.00) = 0.0228
P(X > 110) = P(Z > 2.00) = 1 – P(Z < 2.00) = 1.0 – 0.9772 = 0.0228
P(X < 70) + P(X > 110) = 0.0228 + 0.0228 = 0.0455

(d) P(Xlower < X < Xupper) = 0.70
P(Z < –1.0364) = 0.15 and P(Z < 1.0364) = 0.85

Xlower = 90 – 1.0364(10) = 79.64 and Xupper = 90 + 1.0364(10) = 100.36

6.6 (a) Partial PHStat output:
Common Data
Mean 50
Standard Deviation 4
Probability for a Range
Probability for X <= From X Value 42
X Value 42 To X Value 43
Z Value -2 Z Value for 42 -2
P(X<=42) 0.0227501 Z Value for 43 -1.75
P(X<=42) 0.0228
Probability for X > P(X<=43) 0.0401
X Value 43 P(42<=X<=43) 0.0173
Z Value -1.75
P(X>43) 0.9599 Find X and Z Given Cum. Pctage.
Cumulative Percentage 5.00%
Probability for X<42 or X >43 Z Value -1.644854
P(X<42 or X >43) 0.9827 X Value 43.42059
P(X > 43) = P(Z > – 1.75) = 1 – 0.0401 = 0.9599
(b) P(X < 42) = P(Z < – 2.00) = 0.0228
(c) P(X < A) = 0.05,
A = 50 – 1.645(4) = 43.42
(d) Partial PHStat output:
Find X and Z Given Cum. Pctage.
Cumulative Percentage 80.00%
Z Value 0.841621
X Value 53.36648
P(Xlower < X < Xupper) = 0.60
P(Z < – 0.84) = 0.20 and P(Z < 0.84) = 0.80

Xlower = 50 – 0.84(4) = 46.64 and Xupper = 50 + 0.84(4) = 53.36

6.7 (a) P(X > 31) = P(Z > –0.1375) = 0.5547
(b) P(8< X < 21) = P(–3.0125 < Z < –1.3875) = 0.0813
(c) P(X < 8) = P(Z < –3.0125) = 0.0013
(d) P(X < A) = 0.90 A = 32.1 + 1.2816(8) = 42.35

6.8 (a) P(44 < X < 54) = P(–1.6 < Z < –0.6) = 0.2195
(b) P(X < 25) + P(X > 70) = P(Z < –3.5) + P(Z > 1)
= 0.0002 + (1.0 – 0.8413) = 0.1589
(c) P(X > A) = 0.70 P(Z < –0.5244) 0.30
A = 60 – 0.5244(10) = 54.756 thousand miles or 54,756 miles
(d) The larger standard deviation makes the Z-values smaller.
(a) P(44 < X < 54) = P(–1.33 < Z < –0.5) = 0.2173
(b) P(X < 25) + P(X > 70) = P(Z < –2.92) + P(Z > 0.83)
= 0.0018 + (1.0 – 0.7978) = 0.20141
(c) A = 60 – 0.5244(12) = 53.707 thousand miles or 53,707 miles

6.9 (a) P(X > 80) = P(Z > 1) = 0.1587
(b) P(45 < X < 55) = P(–6< Z < –4) = 0.00003
(c) P(Xlower < X < Xupper) = 0.95

Xlower = 75 – 1.96(5) = $65.2 and Xupper = 75 + 1.96(5) = $84.8

6.10 PHStat output:
Common Data
Mean 73
Standard Deviation 8
Probability for a Range
Probability for X <= From X Value 65
X Value 91 To X Value 89
Z Value 2.25 Z Value for 65 -1
P(X<=91) 0.9877755 Z Value for 89 2
P(X<=65) 0.1587
Probability for X > P(X<=89) 0.9772
X Value 81 P(65<=X<=89) 0.8186
Z Value 1
P(X>81) 0.1587 Find X and Z Given Cum. Pctage.
Cumulative Percentage 95.00%
Probability for X<91 or X >81 Z Value 1.644854
P(X<91 or X >81) 1.1464 X Value 86.15883

6.10 (a) P(X < 91) = P(Z < 2.25) = 0.9878
cont. (b) P(65 < X < 89) = P(– 1.00 < Z < 2.00) = 0.9772 – 0.1587 = 0.8185
(c) P(X > A) = 0.05 P(Z < 1.645) = 0.9500
A = 73 + 1.645(8) = 86.16%
(d) Option 1: P(X > A) = 0.10 P(Z < 1.28) 0.9000

Since your score of 81% on this exam represents a Z-score of 1.00, which is below the minimum Z-score of 1.28, you will not earn an “A” grade on the exam under this grading option.
Option 2:
Since your score of 68% on this exam represents a Z-score of 2.00, which is well above the minimum Z-score of 1.28, you will earn an “A” grade on the exam under this grading option. You should prefer Option 2.

6.11 PHStat output:
(a) P(X < 150) = P(Z < – 1.60) = 0.0548

(b) P(150 < X < 198) = P(– 1.6 < Z < 1.6) = 0.8904

(c) P(X > 198) = P(Z > 1.60) = 0.0548

(d) P(X < A) = 0.01 P(Z < -2.3263) = 0.01
A = 174 – 15(2.3263) = 139.1048 minutes

6.12 (a) P(X > 50) = P(Z > 1.5083) = 0.0657
(b) P(13 < X < 29) = P(–1.575 < Z < –0.2417) = 0.3469
(c) P(X < 13) = P(Z < –1.575) = 0.0576
(d) P(X < A) = 0.95 Z = 1.6449 A = 51.6382 gallons

6.13 (a) Partial PHStat output:
Probability for a Range
From X Value 21.99
To X Value 22
Z Value for 21.99 -2.4
Z Value for 22 -0.4
P(X<=21.99) 0.0082
P(X<=22) 0.3446
P(21.99<=X<=22) 0.3364
P(21.99 < X < 22.00) = P(– 2.4 < Z < – 0.4) = 0.3364
(b) Partial PHStat output:
Probability for a Range
From X Value 21.99
To X Value 22.01
Z Value for 21.99 -2.4
Z Value for 22.01 1.6
P(X<=21.99) 0.0082
P(X<=22.01) 0.9452
P(21.99<=X<=22.01) 0.9370
P(21.99 < X < 22.01) = P(– 2.4 < Z < 1.6) = 0.9370

6.13 (c) Partial PHStat output:
cont.
Find X and Z Given Cum. Pctage.
Cumulative Percentage 98.00%
Z Value 2.05375
X Value 22.0123
P(X > A) = 0.02 Z = 2.05 A = 22.0123
(d) (a) Partial PHStat output:
Probability for a Range
From X Value 21.99
To X Value 22
Z Value for 21.99 -3
Z Value for 22 -0.5
P(X<=21.99) 0.0013
P(X<=22) 0.3085
P(21.99<=X<=22) 0.3072
P(21.99 < X < 22.00) = P(– 3.0 < Z < – 0.5) = 0.3072
(d) (b) Partial PHStat output:
Probability for a Range
From X Value 21.99
To X Value 22.01
Z Value for 21.99 -3
Z Value for 22.01 2
P(X<=21.99) 0.0013
P(X<=22.01) 0.9772
P(21.99<=X<=22.01) 0.9759
P(21.99 < X < 22.01) = P(– 3.0 < Z < 2) = 0.9759
(c) Partial PHStat output:
Find X and Z Given Cum. Pctage.
Cumulative Percentage 98.00%
Z Value 2.05375
X Value 22.0102
P(X > A) = 0.02 Z = 2.05 A = 22.0102

6.14 With 39 values, the smallest of the standard normal quantile values covers an area under the normal curve of 0.025. The corresponding Z value is -1.96. The middle (20th) value has a cumulative area of 0.50 and a corresponding Z value of 0.0. The largest of the standard normal quantile values covers an area under the normal curve of 0.975, and its corresponding Z value is +1.96.

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