Lab3WithSol - Statistics 103 Lab 3 LAB PROBLEMS THESE WILL...

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Statistics 103: Lab 3 LAB PROBLEMS THESE WILL BE ON MIDTERM 1 1. Let Z be a standard normal random variable. Find P ( Z > 0 . 90) and P ( - 1 . 5 Z < 2 . 3). answer: .1841; .9225 2. Let X ∼ N (3 , 9). Find: (a) P (2 < X < 5) (b) P ( X > 0) (c) P ( | X - 3 | > 6) answer: (a) .3779, (b) .8413, (c) .0456 3. Open for student questions. PRACTICE PROBLEMS THESE WILL BE ON MIDTERM 1 1. Let Z be a standard normal random variable (i.e. Z ∼ N (0 , 1)). Find the probability that Z is less than 1 or less than 2. answer: 0.9773 2. Let Z be a standard normal random variable. Find the probability that Z is larger than - 3 or larger than - 2. answer: 0.9987 3. Let Z be a standard normal random variable. (a) Find P ( Z > 0 . 90) (b) Find P ( Z < 0 . 90) (c) Find P (0 Z < 2 . 12) (d) Find P ( - 1 . 5 Z < 2 . 3) (e) Find P (0 > Z > - 1 . 5) (f) Find P ( Z 1 . 53) (g) Find P ( Z > - 0 . 49) (h) Find P (0 . 35 < Z < 2 . 01) (i) Find P ( | Z | > 1 . 28) (j) Find P ( | Z | < 1 . 28) answer: (a) 0.1841, (b) 0.8159, (c) 0.483, (d) 0.9225, (e) 0.4332, (f) 0.937, (g) 0.688, (h) 0.341, (i) 0.2, (j)0.7994 4. Let X ∼ N ( μ, σ 2 ). Find the probability that X is less than σ away from μ . answer: 0.68 5. Let X ∼ N (5 , 100). Find (a) P ( X > 10) (b) P ( - 20 < X < 15) (c) Find the number a such that P ( X > a ) = . 05. answer: 0.3085; 0.8351; 21.5 6. Let X be a normal random variable such that EX = 10 and var( X ) = 36, compute (a) P ( X > 5) (b) P (4 < X < 16) (c) P ( X < 8) (d) P ( X < 20) (e) P ( X > 16) answer: (a) .7977, (b) .6827, (c) .3695, (d) .9522, (e) .1587 PRACTICE PROBLEMS THESE WILL NOT BE COVERED ON MIDTERM 1 1. Let Z be a standard normal random variable. Find the number a such that P ( Z > a ) = 0 . 938. 2. Let Z be a standard normal random variable. (a) Find the number a such that P ( Z a ) = 0 . 648 (b) Find the number a such that P ( | Z | < a ) = 0 . 95 (c) Find the number a such that P ( Z < a ) = 0 . 95 (d) Find the number a such that P ( Z > a ) = 0 . 085 (e) Find the number a such that P ( Z < - a ) = 0 . 023 answer: (a) 0.38, (b) 1.96, (c) 1.645, (d) 1.37, (e)
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