Normal Distribution

Question 1

How do you find the expected value of x in a binomial distribution?

Answer 1

E(x) = np

Question 2

How do you find the variance of a binomial distribution?

Answer 2

Var(x) = np(1-p)

Question 3

How can you tell you have a good approximation for a normal distribution?

Answer 3

np and np(1-p) are both larger than 5

Question 4

What characteristics of n and p will give a good approximation?

Answer 4

n is large
p is close to 0.5

Question 5

Define the central limit theorem

Answer 5

When n>= 30
The sample size is large enough the the sample means can be normally distributed

• this is irrespective of the distribution of the population (it does not have to have been normally distributed beforehand)