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# Normal distribution help watch

1. I got (a) correct.But I can't understand where they got the z=0.3853.How do I find k? Question:
Spoiler:
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3. (Original post by IFoundWonderland)
I got (a) correct.But I can't understand where they got the z=0.3853.How do I find k? Question:
Spoiler:
Show
Okay, so when you see a problem like this, your first step is to define a random variable.

Step 1: define a random variable that is "the height of seven year olds".

Step 2: define the distribution of this random variable: .

Step 3: do your probability stuff. So you understood part (a), that is you wanted to find the probability that this child is taller (so greater) than 122.5 cm. Which is

In this case, you're given the probability and you want to find the height. i.e: you know that . I would definitely advise writing this down. It's basically just saying "the probability that the child is shorter (less than) centimetres is 1.65".

Now every probability has a z-value associated with it. You just need to look into your normal distribution tables and look for the z-value that corresponds to a probability of 0.65. Kind of a "reverse table lookup", if you will.

Sure enough, scanning my table, I see that the table has probabilities of and , so 0.65 is in between there. I can just pick the closes one, so has the associated z-value 0.39.

Standardising my random variable, I get:

But . And you know , so can you solve this equation.

Having just written all of this, I realised that the know-it-alls at IB mandate the use of your graphical calculator, in which case, you should look for the statistics option and look for something called "inverse normal".

Here's a video tutorial as to how to do this with a TI-NSpire here: https://www.youtube.com/watch?v=q72ZWZn_Vz8

Hope this was useful, I know it's a bit long, but do take the time to read through it.
4. Zacken

Thanks so much I already did steps 1-3, but it was that last bit finding the inverse normal that I'd forgotten I needed to do .

You're a superstar
5. (Original post by IFoundWonderland)
Zacken

Thanks so much I already did steps 1-3, but it was that last bit finding the inverse normal that I'd forgotten I needed to do .

You're a superstar
No problem!

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