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stats NIE hw 6

# stats NIE hw 6 - Statistics I Jun Nie RCT Tues 2 3:15...

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Statistics I – Jun Nie RCT: Tues 2 – 3:15 Homework 6 Section 6-2: 4, 6, 8, 12, 16, 18, 24, 30, 32, 36, 40 4. The “Bell Shape” is a symmetrical “hill” with the peak at Z = 0, and tapers off to both sides, approaching zero. The area of the function from -∞ to +∞ approaches 1. 6. p( x > 50.5) = 3* .5 * .5 = .75 8. 51.6 – 51.5 = .1 minutes (.1 / 2) = .05 12. p( Z < 2.5) = .9946 18. p( 0.50 < Z < 1.50 ) = p( Z < 1.5) – p( Z < 0.50) = .9932 - .6915 = .3107 24. p( -3.90 < Z < 1.50) ≈ p( Z < 1.50) = .9932 {because p( Z < 3.90) << 0.001} 30. p(-2 < Z < 2) = 1 - 2p( Z < -2) = 1 – 2(.0228) = .9544 95.44% 32. p(-3.50 < Z < 3.50) = 1 - 2p( Z < -3.50) = 1 – 2(.0001) = .9998 99.98% 36. p( |Z| > 1.96) = 2p(Z < -1.96) = 2(.025) = .05 40. We reject 1% of thermometers that read too high and 1% that read too low. We select the middle 98%. We define: Z* = upper bound, -Z* = lower bound. We accept values of Z that fulfill the following inequality: |Z| < Z* , where p(|Z| < Z*) = .98 p(Z < -Z*) = p(Z > Z*) = .01, we solve for Z*. According to the Z-Score table, we get Z* ≈ 2.33 . {According to a t-table with an area of .02 in two tails, and a large degree of freedom, we arrive at Z* = 2.326} The two reading cutoff values are 2.33 and -2.33 for the upper and lower bounds, respectively. Section 6-3:

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6, 12, 16, 18, 22, 30 6. μ = 100, σ = 15, X = 131.5 Z’ = (x – μ) / σ (131.5 – 100) / 15= 2.10 p(Z > 2.10) = .0179 12. p(Z > Z’) = .15 Z’ ≈ 1.04 X = (σ)( Z*) + μ = (15)(1.04) + 100 = 115.6 16. given: mens height μ = 69, σ = 2.8, womens height μ = 63.6, σ = 2.5 a. Men: Z* = (X – μ)/ σ = (78 – 69.0) / 2.5 = 3.60 .0001 = p(Z > 3.50), thus p(Z > 3.60) < .0001 less than .01% of men do not fit in 78” caskets.
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stats NIE hw 6 - Statistics I Jun Nie RCT Tues 2 3:15...

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