Normal distribution Flashcards

1
Q

normal distribution

A
  • X~N(mu, variance)
  • area under curve = 1
  • symmetrical about mean
  • points of inflection at mu +/- sigma
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2
Q

standard normal distribution

A

X ~ N(0,1)
Z = (X- mu)/sigma

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3
Q

Conditions for binomial approximation

A
  1. n is large
  2. p is close to 0.5
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4
Q

mu and sigma for binomial approximation

A

mu = np
sigma = sqrt(np(1-p))

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5
Q

Finding mu
X~N(mu,9), Given that P(X>20)= 0.2

A

P(Z> (20-mu/3)) = 0.2
P(Z>z)=0.2 where X~N(0,1)
z = 0.8416
using Z = 20-mu/3
mu = 17.5

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6
Q

Finding sigma
X~N(50,variance)
Given that P(X<46)=0.2119

A

P(X<46) = 0.2119
P(Z< (46-50/sigma)=0.2119
Draw a normal diagram with line for z
P(Z<x) = 0.2119
use inverse normal with mu=0,sigma=1 to find x
use Z=(X-mu/sigma) to find sigma

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7
Q

Formulation of hypothesis testing normal distribution problem

A
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8
Q

Formulation of finding critical value for normal distribution problem

A
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