Download Statistics Homework Solutions: Normal Distribution and Confidence Intervals - Prof. Spence and more Assignments Data Analysis & Statistical Methods in PDF only on Docsity! ST 301 Homework 8 Solutions CH 5.2 28.) (a) Given: σX = 10 mg, n = 3 √ σXbar = √ . √ 5 (b) Want: σXbar = √ Solve for n. Explanation: Due to measurement error and natural random variability, a single measurement will not give you the exact true value of what you’re trying to measure. The average of several measurements is more likely to be close to the true mean. 30.) (a) Mass for individual measurements: N(µ=4600, σ=10) Mass for average of 3 measurements: N(µ=4600, σ=5.7735) Red: Individual Measurements Green: Mean of 3 measurements (b) P(X < 4590 OR X > 4610), where X ~ N(4600, 10) = P(X < 4590) + P(X > 4610) = P(Z < ) + P(Z > ), where Z ~ N(0, 1) Standard Normal + P(Z > 7 + (1 ‐ .8 = P(Z < ‐1) 1) = .158 413) = 0.3174 using table A (or about 32% by the 68‐95‐99.7 rule) (c) P( < 4590 OR > 4610), where ~ N(4600, 5.7735) = P( < 4590) + P( > 4610) = P(Z < . ) + P(Z > . ), where Z ~ N(0, 1) Standard Normal 1.73) + P = .0418 4.) ACT Scores ~ approx N(µ=20.8, σ=4.8) = P(Z < ‐ (Z > 1.73) + (1 ‐ .9582) = 0.0836 using table A 3 (a) P(single student ≥ 23) = P(Z ≥ . . ) = P(Z ≥ 0.46) = 0.3428 using table A .8 σ(b) SRS of n=25. µXbar = 20 Xbar = √ . √ . (c) P( ≥ 23) = P(Z ≥ . . ) = P(Z ≥ 2.29) = 0.0 11 using table A t ACT l. The average of a sample of scores, , than the raw scores. So, the probability 36.) (a) µX = 4(0.21) + 3(0.43) + 2(0.30) + 1(0.05) + 0(0.01) = 2.78 σX = √0.7516 (d) We were told tha scores are only approximately norma is also only approximately normal, but it will be closer to normal calculation in (c) is more accurate. . (b) A SRS with n=50. µXbar = µX = 2.78 σXbar = √ . √ = 0.1226 (c) P(X ≥ 3) = 0.43 + 0.21 = 0.64 P( ≥ 3) = P(Z ≥ . . ) = P(Z ≥ 1.79) = 0.0367 using table A 41.) Let X = weight of a given passenger. We are told to assume X is Normal(µ=190 lbs, σ=35 lbs). With n=19 passengers, find P(Total Weight > 4000 lbs) = P( > ) = P( > 210.526).