1. Continuous Probability Distributions Solved Problems
Chapter 7
Continuous Probability Distributions Solved Problems

2. Problem 7-4

3. Problem 7-9 a. 490 and 510, found by 500  1(10)
b. 480 and 520, found by 500  2(10)
c. 470 and 530, found by 500  3(10)

4. Problem 7-11
Adjusting for their industries, Rob is well below average and Rachel well above.

5. Problem 7-13
.1915
.3944
.3944
.3085 12 32 18 25
m = 20
s = 4

6. Problem 7-13 continued

7. Problem 7-17a
.4332
.3944
.3944 18
m = 50
s = 4 55 44

8. Problem 7-17b
.3944
.1056
m = 50
s = 4 55

9. Problem 7-17c
.1915
.3944
.2029 52 55
m = 50
s = 4

10. Problem 7-18a
.1406
.2611
m = 80
s = 14

11. Problem 7-18b
.1406
.3594
X=75
m = 80
s = 14

12. Problem 7-18c
.2611
.2022
.4633 55 70
m = 80
s = 14

13. Problem 7-20a
.1915
.3085 X
X=80,000
=70,000 =20,000
a. p(x > 80,000), Z=(x - ) /  = (80, ,000) / 20,000 = .5
p(x > 80,000) = = .3085

14. Problem 7-20 b
.0987
.1915 X
X=65,000
X+80,000
 =70,000  =20,000
P(65000 < X < 80,000)
Z = (x - ) /  = (65, ,000) / 20,000 = -.25
and Z = (80, ,000) / 20,000 = .50
 P(65,000 <X < 80,000) = = .2902

15. Problem 7-20 c
.0987
X=65,000 X
= 70,000 = 20,000
P(X > 65,000)
Z = (x - ) /  = (65, ,000) / 20,000 = -.25
P(X > 65,000) = = .5987

16. Problem 7-21a .4236 .0764 x  = 15 = 3.5 P(x > 20)
Z = (x - ) / = ( ) / 3.5 = 1.43
P(x > 20) = = .0764

17. Problem 7-21 b
.4236 X
 = 15,  = 3.5
X=20
P( x < 20)
Z = (x - ) /  = ( ) / 3.5 = 1.43
 P(x < 20) = = .9236

18. Problem 7-21 c .4236 .1185 P(10 < x < 12)
. 3051
X=10
X=12
 = 15  = 3.5
P(10 < x < 12)
Z = ( x -  ) /  = (10-15) / 3.5 = and Z = (12-15) / 3.5 = -.86
 P(10 < x < 12) = = .1185

19. Problem 7-23
m = 50
s = 4
x=? x

20. Problem 7-24
.30
.20
X=?
m = 80
s = 14

21. Problem 7-26
.45
.05
m = 1200
s = 225
x=?
1.645

22. Problem 7-29
.30
.20
= x = 215
= 17 Z
.84

23. Problem 7-30
.49
.01
= 12,200
= 820 Z

24. Problem 7-31a

25. Problem 7-31b
.2422
.2578
14.5
m=12.5
s=3.062

26. Problem 7-31c
.2422
.2578
10.5
m=12.5
s=3.062

27. Problem 7-32a

28. Problem 7-32b
.2852
.2148
24.5
m=22
s=3.15

29. Problem 7-32c
.4803
.0197
15.5 x
m=22
s=3.15

30. Problem 7-32d
.4913
.3665
14.5
25.5 X 15 X 25
m=22
s=3.15

31. Problem 7-41
.1554
.5000
170 x
m=180
s=25

32. Problem 7-41(continued)
.4982
.0018
m=1500
s=120
1850