# Finding probablity using the standard normal distribution

• Apr 14th 2009, 11:05 PM
rennstimpie
Finding probablity using the standard normal distribution
Can anyone help with the problems below? Please explain, if possible.

Calculate the following probabilities:

i. P(0£ z £ 2.3)
ii. P(0£ z £1.68)
iii. P(0.24£ z £.0.33)
iv. P(-2.58 £ z £ 0)
v. P(-2.81 £ z £. -1.35)
vi. P(-0.73 £ z £ 0.49)
vii. P(z ³ 1.7 )
viii. P(z ³ -0.95)
ix. P( z £ - 1.96) x. P(-1.4 £ z £ 1.55)

How do you work these out? I'm lost.
• Apr 15th 2009, 10:52 AM
Twig
Hi

You do pretty much the same thing for all of these.
I assume you have some basic knowledge here, understandning that you
have a normalized variable z, with mean 0 and standard deviation 1.

$\displaystyle P(0 \leq z \leq 2.3)$ can be calculated using a distribution table. (Google, wikipedia etc).

In this you look up that the probability that $\displaystyle z \leq 2.3$ is approximately 0.9893.

But you have also that $\displaystyle 0 \leq z$ .
And $\displaystyle P(0 \leq z) = 0.5$

So 0.9893-0.5 = 0.4893