chapter 1

Chapter 4: Continuous Random Variables and Probability DistributionsSection 4.326.a. P(0 ≤ Z ≤ 2.17) = Φ(2.17) - Φ(0) = .4850b. Φ(1) - Φ(0) = .3413c. Φ(0) - Φ(-2.50) = .4938d. Φ(2.50) - Φ(-2.50) = .9876e. Φ(1.37) = .9147f. P( -1.75 < Z) + [1 – P(Z < -1.75)] = 1 - Φ(-1.75) = .9599g. Φ(2) - Φ(-1.50) = .9104h. Φ(2.50) - Φ(1.37) = .0791i. 1 - Φ(1.50) = .0668j. P( |Z| ≤ 2.50 ) = P( -2.50 ≤ Z ≤ 2.50) = Φ(2.50) - Φ(-2.50) = .987627.a. .9838 is found in the 2.1 row and the .04 column of the standard normal table so c = 2.14.b. P(0 ≤ Z ≤ c) = .291 ⇒ Φ(c) = .7910 ⇒ c = .81c. P(c ≤ Z) = .121 ⇒ 1 - P(c ≤ Z) = P(Z < c) = Φ(c) = 1 - .121 = .8790 ⇒ c = 1.17d. P(-c ≤ Z ≤ c) = Φ(c) - Φ(-c) = Φ(c) – (1 - Φ(c)) = 2Φ(c) – 1⇒ Φ(c) = .9920 ⇒ c = .97e. P( c ≤ | Z | ) = .016 ⇒ 1 - .016 = .9840 = 1 – P(c ≤ | Z | ) = P( | Z | < c )= P(-c < Z < c) = Φ(c) - Φ(-c) = 2Φ(c) – 1⇒ Φ(c) = .9920 ⇒ c = 2.41141