MATH 214 Probability and Statistics for Business Majors
Dr. Ed Donley
Answers to Problems
2.3 a)
Frequency Distribution
|
Years |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
Frequency |
8 |
7 |
6 |
4 |
4 |
2 |
0 |
0 |
1 |
Relative Frequency Distribution
|
Years |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
Relative Frequency |
.25 |
.22 |
.19 |
.13 |
.13 |
.06 |
0 |
0 |
.03 |
Cumulative Distribution
|
Years |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
Frequency |
8 |
15 |
21 |
25 |
29 |
31 |
31 |
31 |
32 |
Cumulative Relative Distribution
|
Years |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
Frequency |
.25 |
.47 |
.66 |
.78 |
.91 |
.97 |
.97 |
.07 |
1.00 |
c) 17, .53
d) 29, .91
2.17 Sample A: x = 10, s2 = 25, s = 5
Sample B: x = 10, s2 = 25, s = 5
2.20 above 80
2.21 84%. If the salary distribution is bell-shaped, 97.5%.
3.10 a) 0.10
b) 0.10
c) 0.50
d) 0.40
5.8
|
x |
0 |
1 |
2 |
3 |
4 |
|
P(x) |
1/16 |
4/16 |
6/16 |
4/16 |
1/16 |
m = 2, s2 = 1, s = 1
5.26 a) 0.4305
b) 7.2
c) 0.30
5.33 a) 0.40745
b) 0.18411
c) 0.09963
6.18 a) .1587
b) .0668
c) .0122
d) .8413
e) .9332
f) .9878
g) .1587
h) .0668
i) .0122
j) .1465
k) .0919
l) .7745
m) .7745
6.19 a) .8413
b) .7881
c) .0532
d) .4772
e) .1498
6.20 a) s = 10
b) s = 10
c) m = 20 or m = 30
d) s = 11.36
6.23 P(30 < x) = .1036
P(35 < x) = .0301
P(x < 15) = .2643
P(15 < x < 25) = .4714
6.24 a) .7483
b) .0918
6.25 60 in statistics is equivalent to 76 in accounting.
80 in accounting corresponds to z = 1.11 and 65 in statistics corresponds to z = 1, so the accounting score is higher.
6.28 0.0488 feet
7.23 a) P(xbar > 18.75) = 0.50, P(xbar > 19.00) = 0..3897, P(xbar > 19.50) = 0..3033
b) 894
7.24 a) 0.1075
b) 894
8.14 a) [17.84, 28.56]; [-infinity, 27.55]; [18.85, infinity]
b) [96.72, 105.28]; [-infinity, 104.29]; [97.71, infinity]
c) [-9.4, 14.6]; [-infinity, 9.96]; [-4.76, infinity]
d) [483.3, 550.7]; [-infinity, 545.2]; [488.8, infinity]
8.15 [65.21, 79.67]
8.18 102, 0.505
8.19 a) [46.41, 63.31]
b) [-infinity, 61.12]
c) [48.60, infinity]
8.22 a) No. [-8.78, 24.78]
b) Any confidence level above 80%.
10.4 113 miles