Normal distribution

Question 1

Symbols for normal distribution

Answer 1

μ is the mean
σ2 is the variance
σ is the standard deviation

Question 2

The continuous random variable can follow a normal distribution if:

Answer 2

• The distribution is symmetrical
• The distribution is bell-shaped

Question 3

When can I use a normal distribution to approximate a binomial distribution?

Answer 3

• n is large (large number of trials)
• p is close to 0.5

Question 4

The mean and variance of a binomial distribution can be calculated by:

Answer 4

μ=np
σ^2=np(1-p)

Question 5

How do I approximate a probability?

Answer 5

STEP 1: Find the mean and variance of the approximating distribution
STEP 2: Apply continuity corrections to the inequality
STEP 3: Find the probability of the new corrected inequality
Use the “Normal Cumulative Distribution” function on your calculator
The probability will not be exact as it is an approximate but provided n is large and p is close to 0.5 then it will be a close approximation