Section 6.2 Lecture Problems

Section 6.2 Lecture Problems - Solutions for Lecture...

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Solutions for Lecture Problems from Section 6.2 19.Let x be the continuous r.v. of the rainfall (in inches) in Dallas, Texas, during April. Given: μ = 3.5 in σ = 0.8 in x is normal a. Want Prob ( x > 5 in) 5.0 3.5 1.88 .8 z - = Prob ( x > 5.0) = Prob ( z > 1.88) = 1 – Prob ( z < 1.88) = 1 – 0.9699 = 0.0301 The rainfall exceeds 5 inches in 3.01% of all Aprils. b. Want Prob ( x < 3 in) 3 3.5 .63 .8 z - = ≈ - Prob ( x < 3.0) = Prob ( z < -0.63) = 0.2643 Also note that by the symmetry of the normal curve Prob ( z < -0.63) = Prob ( z > 0.63) = 1 – Prob ( z < 0.63) = 1 – 0.7357 = 0.2643 The rainfall is less than 3 inches in 26.43% of all Aprils. c. “Extremely wet” month if total April rainfall is in the upper 10% of the distribution. Want the value of x * so that Prob ( x x *) = 0.10
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Top 10% of rainfall in all Aprils means upper 10% of the normal curve, in the right tail. Right tail area = Prob ( z z *) = 0.10 For what value of z * is Prob ( z z *) = 0.10? If the area in the right tail = 0.10, then the area under to left is 1 – 0.10 = 0.90. From z table, find the value of z * so that Prob ( z z *) = 0.90?
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