CIE A Level Maths: Probability & Statistics 1复习笔记3.4.2 Normal Approximation of Binomial

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

Why do we use approximations?

• If there are a large number of values for a binomial distribution there could be a lot of calculations involved and it is inefficient to work with the binomial distribution
  • These days calculators can calculate binomial probabilities so approximations are no longer necessary
  • However it is easier to work with a normal distribution
    • You can calculate the probability of a range of values quickly
    • You can use the inverse normal distribution function (most calculators don't have an inverse binomial distribution function)
• In your exam you must use the formula and not a calculator to find binomial probabilities so you are limited to small values of n

What are continuity corrections?

• The binomial distribution is discrete and the normal distribution is continuous
• A continuity correction takes this into account when using a normal approximation
• The probability being found will need to be changed from a discrete variable, X,   to a continuous variable, X_N

How do I apply continuity corrections?

• Think about what is largest/smallest integer that can be included in the inequality for the discrete distribution and then find its upper/lower bound
• 

How do I approximate a probability?

• STEP 1: Find the mean and variance of the approximating distribution