Stats Assignment 8

a. Pr(Z ≥ -2.98) = 0.9986 i. I used the same method as question 2, the Compliment rule: 𝑃𝑟(𝑍 ≥− 2. 98) = 1 − 𝑃𝑟(𝑍 ≤− 2. 98) = 1 − Φ(− 2. 98) = 1 − 0. 0014 = 0. 9986 Do the same for the following below. Note however that they are no longer Standard Normal Distributions. 7. X ~ Norm(266, 162), find Pr(X < 200) a. Pr(X < 200) = 𝑃𝑟( 𝑋−266 16 < 200−266 16 ) = 𝑃𝑟(𝑍 <− 4. 125 = Φ(− 4. 125) = 0 i. To standardize, I subtracted the mean and dividing by the standard error to find the probability. 8. X ~ Norm(-2, 52), find Pr(-4 < X < -3) Pr(-4 < X < -3) = 𝑃𝑟(− 4 < 𝑋𝑋 <− 3) = 𝑃𝑃𝑃𝑃/ −4 5 < (−𝑋)𝑋−(−2) 5 < (−3)−(−2) 5 / = 𝑃𝑃𝑃𝑃 < −2𝑋𝑋−(−2) 5 < −1 5 / = Φ/ −1 5 / − Φ/ −2 5 / = 0. 4207 − 0. 3446 = 0. 0761. i. I did the same thing by standardizing and then taking the difference in the values. Φ 9. X ~ Norm(-2, 52), find Pr(X = -3) a. Pr(X = -3) = 0 i. Just like before, the probability of any continuous variable is always 0. 10. X ~ Norm(64.4, 2.42), find Pr(|X| > 70) a. Pr(|X| > 70) = .009815 i. This probability has to get split up into two and then you must add them together by using the compliment method rule on one and then the standard form on the other.