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Math 203_Lecture 8

# Math 203_Lecture 8 - Principles of Statistics 1 Lecture 8...

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Principles of Statistics 1 Lecture 8: Math 203 Abbas Khalili Department of Mathematics and Statistics McGill University May 12, 2011 Principles of Statistics 1 Lecture 8: Math 203 – p. 1/3

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Approximating a Binomial distribution Remember the Food and Drug Administration (FDA) example in Lecture 15, Chapter 4: Principles of Statistics 1 Lecture 8: Math 203 – p. 2/3
Approximating a Binomial distribution Remember the Food and Drug Administration (FDA) example in Lecture 15, Chapter 4: We had a Binomial random variable X with parameters n = 800 and p = 0 . 35 . Principles of Statistics 1 Lecture 8: Math 203 – p. 2/3

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Approximating a Binomial distribution Remember the Food and Drug Administration (FDA) example in Lecture 15, Chapter 4: We had a Binomial random variable X with parameters n = 800 and p = 0 . 35 . Wanted to calculate P (270 X 290) Principles of Statistics 1 Lecture 8: Math 203 – p. 2/3
Approximating a Binomial distribution Remember the Food and Drug Administration (FDA) example in Lecture 15, Chapter 4: We had a Binomial random variable X with parameters n = 800 and p = 0 . 35 . Wanted to calculate P (270 X 290) The table for Binomial in the back of the text book DOES NOT HAVE the case n = 800 . Principles of Statistics 1 Lecture 8: Math 203 – p. 2/3

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Approximating a Binomial distribution Remember the Food and Drug Administration (FDA) example in Lecture 15, Chapter 4: We had a Binomial random variable X with parameters n = 800 and p = 0 . 35 . Wanted to calculate P (270 X 290) The table for Binomial in the back of the text book DOES NOT HAVE the case n = 800 . Can we approximate the above probability? Principles of Statistics 1 Lecture 8: Math 203 – p. 2/3
Histograms of the Bin(800, 0.35) Binom(800,0.35) y Frequency 240 260 280 300 320 0 500 1000 1500 Principles of Statistics 1 Lecture 8: Math 203 – p. 3/3

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Approximating a Binomial distribution As you can see the distribution of the Binomial under consideration is mound-shaped and symmetric. Principles of Statistics 1 Lecture 8: Math 203 – p. 4/3
Approximating a Binomial distribution As you can see the distribution of the Binomial under consideration is mound-shaped and symmetric. Can we approximate the distribution of the X by a normal distribution? Principles of Statistics 1 Lecture 8: Math 203 – p. 4/3

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Approximating a Binomial distribution As you can see the distribution of the Binomial under consideration is mound-shaped and symmetric. Can we approximate the distribution of the X by a normal distribution? Note that if X Bin ( n, p ) then μ = E ( X ) = n × p , σ 2 = V ar ( X ) = n × p × (1 - p ) . Principles of Statistics 1 Lecture 8: Math 203 – p. 4/3
Approximating a Binomial distribution As you can see the distribution of the Binomial under consideration is mound-shaped and symmetric. Can we approximate the distribution of the X by a normal distribution? Note that if X Bin ( n, p ) then μ = E ( X ) = n × p , σ 2 = V ar ( X ) = n × p × (1 - p ) .

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