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
2
Q
standard normal distribution
A
X ~ N(0,1)
Z = (X- mu)/sigma
3
Q
Conditions for binomial approximation
A
- n is large
- p is close to 0.5
4
Q
mu and sigma for binomial approximation
A
mu = np
sigma = sqrt(np(1-p))
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
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
7
Q
Formulation of hypothesis testing normal distribution problem
A
8
Q
Formulation of finding critical value for normal distribution problem
A