Continuous Probability Distributions Solved Problems

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Presentation transcript:

Continuous Probability Distributions Solved Problems Chapter 7 Continuous Probability Distributions Solved Problems

Problem 7-4

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)

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

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

Problem 7-13 continued

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

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

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

Problem 7-18a .1406 .2611 75 90 m = 80 s = 14

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

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

Problem 7-20a .1915 .3085 X X=80,000 =70,000 =20,000 a. p(x > 80,000), Z=(x - ) /  = (80,000 - 70,000) / 20,000 = .5 p(x > 80,000) = .5000 - .1915 = .3085

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 - 70,000) / 20,000 = -.25 and Z = (80,000 - 70,000) / 20,000 = .50  P(65,000 <X < 80,000) = .0987 + .1915 = .2902

Problem 7-20 c .0987 X=65,000 X = 70,000 = 20,000 P(X > 65,000) Z = (x - ) /  = (65,000 - 70,000) / 20,000 = -.25 P(X > 65,000) = .0987 + .5000 = .5987

Problem 7-21a .4236 .0764 x  = 15 = 3.5 P(x > 20) Z = (x - ) / = (20 - 15) / 3.5 = 1.43 P(x > 20) = .5000 - .4236 = .0764

Problem 7-21 b .4236 X  = 15,  = 3.5 X=20 P( x < 20) Z = (x - ) /  = (20 - 15) / 3.5 = 1.43  P(x < 20) =.4236 +. 5000 = .9236

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 = -1.43 and Z = (12-15) / 3.5 = -.86  P(10 < x < 12) = .4236 - .3051 = .1185

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

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

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

Problem 7-29 .30 .20 = 200 x = 215 = 17 Z .84

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

Problem 7-31a

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

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

Problem 7-32a

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

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

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

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

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