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# hw6sol - left of z is 0.90 This z is 1.28 Then we solve the...

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Solutions to Homework 6 Problem 6.11 a. P ( z ≤ - 1 . 0) = 0 . 1587 b. P ( z ≥ - 1) = 1 - 0 . 1587 = 0 . 8413 c. P ( z ≥ - 1 . 5) = 1 - 0 . 0668 = 0 . 9332 d. P ( - 2 . 5 z ) = 1 - 0 . 0062 = 0 . 9938 e. P ( - 3 < z 0) = 0 . 5000 - . 0013 = 0 . 4987 Problem 6.13 a. P ( - 1 . 98 z 0 . 49) = 0 . 6879 - 0 . 0239 = 0 . 6640 b. P (0 . 52 z 1 . 22) = 0 . 8888 - 0 . 6985 = 0 . 1903 c. P ( - 1 . 75 z ≤ - 1 . 04) = 0 . 1492 - 0 . 0401 = 0 . 1091 Problem 6.15 a. z = - 0 . 80 b. If the area between z and - z is 0.9030, then the area less than - z and greater than z is 1 - 0 . 9030 = 0 . 0970. So the area just less than - z is 0 . 0970 2 = 0 . 0485. So - z = - 1 . 66 and z = 1 . 66. c. If the area between z and - z is 0.2052, then the area less than - z and greater than z is 1 - 0 . 2052 = 0 . 7948. So the area just less than - z is 0 . 7948 2 = 0 . 3974. So - z = - 0 . 26 and z = 0 . 26. d. z = 2 . 56 e. If the area to the right of z is 0.6915, then the area to the left of z is 1 - 0 . 6915 = 0 . 3085. So z = - 0 . 50. Problem 6.19 Here we have a normal distribution with μ = 3 . 5 inches and σ = 0 . 8 inches. a. P ( x > 5) = P ( z > 5 - 3 . 5 0 . 8 ) = P ( z > 1 . 8) = 1 - 0 . 9699 = 0 . 0301. So 3.01%. b. P ( x < 3) = P ( z < 3 - 3 . 5 0 . 8 ) = P ( z < - 0 . 63) = 0 . 2643. So 26.43%. 1

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c. First, we need to find z such that the area to the right of
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Unformatted text preview: left of z is 0.90. This z is 1.28. Then we solve the equation below for x . x-3 . 5 . 8 = 1 . 28 So x = (1 . 28)(0 . 8) + 3 . 5 = 4 . 52 inches. Problem 6.21 First, we need to nd z such that the area to the right of z is 0.02 and the area to the left of z is 0.98. This z is 2.05. Then we solve the equation below for x . x-100 15 = 2 . 05 So x = (2 . 05)(15) + 100 = 130 . 75. Problem 6.25 Here we have a normal distribution with = 6 . 8 hours and = 0 . 6 hours. a. P ( x &amp;gt; 8) = P ( z &amp;gt; 8-6 . 8 . 6 ) = P ( z &amp;gt; 2) = 1-. 9772 = 0 . 0228 b. P ( x 6) = P ( z 6-6 . 8 . 6 ) = P ( z -1 . 33) = 0 . 0918 c. P (7 &amp;lt; x &amp;lt; 9) = P ( 7-6 . 8 . 6 &amp;lt; z &amp;lt; 9-6 . 8 . 6 ) = P (0 . 33 &amp;lt; z &amp;lt; 3 . 67) = 0 . 9998-. 6293 = . 3705 2...
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