Lab3 - Statistics 103: Lab 3 LAB PROBLEMS THESE WILL BE ON...

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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). 2. Let X ∼ N (3 , 9). Find: (a) P (2 < X < 5) (b) P ( X > 0) (c) P ( | X - 3 | > 6) 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. 2. Let Z be a standard normal random variable. Find the probability that Z is larger than - 3 or larger than - 2. 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) 4. Let X ∼ N ( μ,σ 2 ). Find the probability that X is less than σ away from μ . 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. 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) 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
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Lab3 - Statistics 103: Lab 3 LAB PROBLEMS THESE WILL BE ON...

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