A-Level Maths: N2-07 Normal Distribution: Inverse Normal Example

[@christohargreaves5234]

been studying A2 maths without a teacher since Christmas, really thankful for the help

[@usamaahmed4982]

Thank you sir for helping me throughout my a levels

[@luketodd8634]

I wish I found your channel sooner!

[@OtterFan48]

great video, thanks. Was really struggling with this but not anymore thanks to you!

[@sherlyns8203]

Hello Jack, my calculator (Casio fx-9750Gii) can work out the inverse norm in both directions if I specify whether the tail is on the left or on the right (whether the inequality is pointing left or right). Just out of interest, does the classwiz calculator that you are utilising just not have this function, or is there a specific reason why you teach us to use just one direction and work out the probability ourselves when the inequality is 'greater than' which will help us answer exam questions? Thanks :)

[@TLMaths]

The casio classwiz calculator only does inverse normal for areas to the left, so that's why I've got to do it that way.

[@guy3854]

Ur actually a lifesaver

[@_stripyzebra7949]

As you said that the 'area' refers to the left side of the value we're looking at, for q3) could you just have looked at 10-c being 0.4 and work with that, instead of doing what you did with 10+c being 0.6? Thanks.

[@TLMaths]

Yes you can do it that way instead

[@jamminermit]

For question 3, what would we do if the values weren’t so easy to calculate? For example, if we were looking at p(12.6-2c

[@TLMaths]

Off the top of my head, I'm not sure how you would go about it without integrating the normal distribution function. I put this into wolframalpha: www.wolframalpha.com/input/?i=int((1%2F(0.5*sqrt(2*pi)))*exp(-((x-10)%5E2)%2F(2*0.5%5E2)),x%3D12.6-2c,11.9%2Bc)%3D0.2 it comes out with c = 1.0895...

[@jamminermit]

TLMaths oh ok, fair enough. Thanks!

[@jamminermit]

Thought this might interest you. I asked this question on the stack exchange, and this method came up to solve it: math.stackexchange.com/questions/3304432/given-the-area-between-two-values-on-a-normal-distribution-how-would-you-use-th/3304739#3304739

[@TLMaths]

That's clever - effectively saying that one of the inequalities is as close to 1 as you like.

[@myckeydoesntwork3907]

Great vid, all makes sense now!

[@dndnddndidbsh709]

What would you do If you were given P(X

[@TLMaths]

That's just asking to find a probability, so use the normalcd function.

[@najukeshwala6634]

How did you inverse 0.6 in the last question?

[@TLMaths]

Go to Inverse Normal and put the area as 0.6 with mean=10 and standard deviation=0.5