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Normal distribution help

IFoundWonderland

I got (a) correct.But I can't understand where they got the z=0.3853.How do I find k? :cry2:

Question:

Spoiler

normaldistributionanswer.png184.7KB

Answer:

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? :cry2:

Question:

Spoiler

Okay, so when you see a problem like this, your first step is to define a random variable.

Step 1: define a random variable

X

that is "the height of seven year olds".

Step 2: define the distribution of this random variable:

X \sim N(117, 5^2)

.

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

\mathbb{P}(X \geq 122.5)

In this case, you're given the probability and you want to find the height. i.e: you know that

\mathbb{P}(X \leq k) = 0.65

. I would definitely advise writing this down. It's basically just saying "the probability that the child is shorter (less than)

k

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

0.6480

and

0.6517

, so 0.65 is in between there. I can just pick the closes one, so

0.6517

has the associated z-value 0.39.

Standardising my random variable, I get:

\mathbb{P}(X \leq k) = \mathbb{Z}\left(Z \leq \frac{k - 117}{5}\right) = 0.65

But

z = \frac{k-117}{5}

. And you know

z

, 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. :smile: