Chap005

# Chap005 - CHAPTER 5—Continuous Random Variables 5.1...

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Unformatted text preview: CHAPTER 5—Continuous Random Variables 5.1 Intervals of values. 5.2 By finding areas under the curve. 5.3 f ( x ) ≥ 0 for all x; area under the curve equals 1. 5.4 Relative likelihood that x will be near the given point. 5.5 When a variable has a rectangular distribution over a certain interval. 5.6 MTB > cdf cl; SUBC> uniform 2.0 8.0. CONTINUOUS UNIFORM ON 2.0 TO 8.0 K P( X LESS OR = K) 0.0000 0.0000 0.5000 0.0000 1.000 0 0.0000 1.5000 0.0000 2.0000 0.0000 2.5000 0.0833 3.0000 0.1667 3.5000 0.2500 4.0000 0.3333 4.5000 0.4167 5.0000 0.5000 5.5000 0.5833 6.0000 0.6667 6.5000 0.7500 7.0000 0.8333 7.5000 0.9167 8.0000 1.0000 a. f ( x ) = 1 8– 2 = 1 6 for 2 ≤ x ≤ 8 = 0 otherwise b. Graph not included in this manual. c. P (3 ≤ x ≤ 5) = P ( x ≤ 5) – P ( x ≤ 3) = .5 – .1667 = .3333 d. P (1.5 ≤ x ≤ 6.5) = P ( x ≤ 6.5) – P ( x ≤ 1.5) = .75 – 0 = .75 e. f. P (1.536 ≤ x ≤ 8.464) = P ( x ≤ 8) = 1 59 Chapter 5: Continuous Random Variables 5.7 3297 . 6703 . 1 ) 100 ( 250 / 100 =- =- = ≤ ≤- e e x P 5.8 a. for 0 ≤ x ≤ 6. = 0 otherwise b. f(x) 1/6 0 6 min c. d. e. 5.9 a. b. 5.10 5 2 2 1 5 1 2 1 1 ) ( =- =- = c d x f 5.11 a. for 120 ≤ x ≤ 140 20 1 120 140 1 1 ) ( =- =- = c d x f b. f(x) 1/20 120 140 min c. P(125 ≤ x ≤ 135) = 10 (1/20) = .5 d. P(x ≥ 135) = 5 (1/20) = .25 5.12 a. 60 7735 . 5 12 120 140 12 130 2 140 120 2 =- =- = = + = + = c d d c x x σ μ Chapter 5: Continuous Random Variables b. 5.13 6 1 12 2 2 1 5 17 1 2 1 1 ) ( = =- =- = c d x f 5.14 a. for 3 ≤ x ≤ 6. b. f(x) 1/3 3 6 inches c. P ( x ≥ 4) = 1 – P ( x < 4) = 1 – .3333 = .6667 P ( x ≥ 5) = 1 – P ( x < 5) = 1 – .6667 = .3333 5.15 a. b. P (2.768 ≤ x ≤ 6.232) = P (3 ≤ x ≤ 6) = 1 [ μ x ± σ x ] = [4.5 ± .8660] = [3.634, 5.366] 5.16 See page 194 of text. 5.17 a. center b. spread 5.18 68.26%, 95.44%, 99.73% 5.19 Subtract the mean and divide the result by the standard deviation; tells us the number of standard deviations the value is above or below the mean. 5.20 a. x equals the mean b. x greater than the mean c. x less than the mean 61 57735 . 20 1 ) 2265 . 124 7735 . 135 ( ) 7735 . 135 2265 . 124 ( 7735 . 135 7735 . 5 130 2265 . 124 7735 . 5 130 =- = ≤ ≤ = + = + =- =- x x P x x x x σ μ σ μ Chapter 5: Continuous Random Variables 5.21 The normal table provides the areas under the standard normal curve (the distribution of the z values). 5.22 a. b. 62 3297 . 6703 .1 )100 ( 250 /100 =- =- = ≤ ≤- e e x P 20 30 Chapter 5: Continuous Random Variables c. 5.23 a. ; x is one standard deviation below the mean. b. ; x is three standard deviations below the mean. c. ; x is equal to the mean. d. ; x is two standard deviations above the mean....
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Chap005 - CHAPTER 5—Continuous Random Variables 5.1...

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