Normal Approximation of the Binomial Distribution, example 1

In this video, we show show how to use the normal distribution to approximate binomial probability. We will use a typical z table along with the formulas for mean and standard deviation of a binomial random variable. Additionally, we will make use of something called continuity correction to improve the approximation.
This video is part of the content available for free at www.statsprofe...

[@j.o.s.h.o]

wow this actually made complete sense. You are a legend sir, my midterm is in 3 hours and you just got me some more marks for sure! Thank you

[@zhch459]

Wow I finally understand the continuity correction! Thanks a lot!

[@Thomas-rv7mq]

Dude you are awesome at explaining!

[@dmcguckian]

Thank you!

[@zanabhafz3953]

You laterally safe my life ❤thanks

[@smoothbird1176]

Perfect video, explanation and demonstration.

[@dmcguckian]

Thank you 🙏

[@umar-tariq]

Can you please explain why did you subtracted prob from 0.5 and not from 1?

[@speconcloud9]

yes, I have the same question @dmcguckian

[@luisiglesias-villacorta5043]

my teacher reviewed this topic for an hour and I left more confused than I was before the introduction to the topic. i watched this 15 minute video and im a nominee for the nobel.

[@dmcguckian]

😀 I am glad it was helpful! Good luck on your exam!

[@yashjain1492]

Great explaination 👍👍

[@dmcguckian]

Glad it was helpful!

[@cesaraugustoruiz]

Great explanation

[@furkanates6951]

thats a good explaination sir, thank you so much

[@vivianakech4258]

thank you!.you made it so simpe

[@dmcguckian]

No problem 😊

[@anancha5915]

very useful ,thank you

[@dmcguckian]

You’re welcome

[@tifaneymarcos5944]

Thank you

[@dmcguckian]

You’re welcome!

[@lakshyabirla2214]

Thanks a lot

[@dmcguckian]

You’re welcome

[@debatradas1597]

Thanks

[@dmcguckian]

You’re welcome

[@pratyasha279]

What's the point of finding the z score exactly?

[@dmcguckian]

The z score enables us to look up the probability using a z table (or Calculus or an app that calculates the area under the normal curve). Without the z value, we would have to use the binomial distribution which is computationally difficult even for powerful computers. It’s less of an issue with today’s computers but it used to be near impossible to do the calculations by hand for problems with large n values. Even fairly powerful computers struggle to do the work quickly, so programmers might still opt to use approximations like this in their code when speed is more important than precision.

[@habeeb3789]

my z table starts from .5000 not .0000

[@dmcguckian]

There are several different z tables, so the thing is to create your drawing and then look at what area your table is designed to give you. You’ll be able to use your table to get either the area you want directly or the table will provide you with a useful area that will enable you to find what you’re looking for.

[@kamleshnakum7500]

Lol

[@ccuuttww]

U don't say the experiment follow binomial distribution at the beginning

[@dmcguckian]

Jill Valentine yes, that’s true. It’s a video in the section of my website covering this topic, so it’s understood from the context. Here on TH-cam, that context is lacking.

[@ccuuttww]

@@dmcguckian haha which is not really true because this method also work with unknown distribution so we don't care where the random variables come form we only care it is IID

[@ccuuttww]

@@dmcguckian and 1 things how can we calculate in case of x=17
with standard normal approximation?

[@dmcguckian]

@@ccuuttww In order to assume the values for the mean and variance are n*p and np(1-p), we would need to know that independent, identically distributed set of values is from the binomial distribution. Also, the binomial distribution ensures the independence of the individual trials, so it is useful information.

[@dmcguckian]

@@ccuuttww If you are asking how to handle the case where x = 17 using the same method, you can calculate the area between 16.5 and 17.5. Everything else remains the same.