Normal distribution

Question 1

normal distribution

Answer 1

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

Question 2

standard normal distribution

Answer 2

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

Question 3

Conditions for binomial approximation

Answer 3

1. n is large
2. p is close to 0.5

Question 4

mu and sigma for binomial approximation

Answer 4

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

Question 5

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

Answer 5

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

Question 6

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

Answer 6

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

Question 7

Formulation of hypothesis testing normal distribution problem

Question 8

Formulation of finding critical value for normal distribution problem