Why is the normal probability curve used to approximate the binomial probability distribution?

manpreet Best Answer 2 years ago

Background: I'm a psychology/behavioural science student. I'm trying to teach myself some stats stuff which goes beyond the scope of my current syllabus.

Question: Quoting from Chapter 6: The Normal Probability Distribution, Introduction to Probability and Statistics by Mendenhall, Beaver and Beaver (14th Ed.),

Since the normal distribution is continuous, the area under the curve at any single point is equal to 00. Keep in mind that this result applies only to continuous random variables. Because the binomial random variable xx is a discrete random variable, the probability that xx takes some specific value—say, x=11x=11 —will not necessarily equal 00.

As far as my understanding goes, the normal probability distribution is used for continuous random variables (as also stated above), so why is it being used for approximating binomial probability distributions, which are discrete random variables? How is this approximation justified when a discrete random variable is capable of taking a certain value with a specific probability, but for a continuous random variable, the probability of it taking a specific value is 00?

Extra: Kindly suggest corrections for the above question in case of erroneous statements.