Inverse Standard Normal Distribution

[orangez]

I need help with the following questions:

Using Z ~ N(0,1), find k such that:

a) Pr(|Z| < k) = 0.85
b) Pr(|Z| > k) = 0.05
c) Pr(|Z| < k) = 0.88
d) Pr(|Z| > k) = 0.1

Thanks in advance 

[Collin Li]

basically means:

, and


This is .

Now use symmetry and complements, as necessary, to solve.

For example, for a)





Hence,

[orangez]

Using invNorm(0.85) i get 1.036, but that's not the correct answer 
The answer is 1.44 

[orangez]

Mind showing me how to do one of the questions? ^^

[Collin Li]

Yeah sorry, I fixed that

[orangez]

LOL!! Thanks Coblin... thought you finished ur posting before i posted

[orangez]

Btw, why did you divide 0.85 by 2 and then add 0.5?

[Collin Li]

If you think about it graphically, dividing 0.85 by 2 will give me instead of from -k to k. Now I can add 0.5 (all of the first half, negative infinity to zero), so I get in total.

[orangez]

Thanks for the explanation.

Can you show me the steps to do b or d (which ever one you fancy)? I just wanna make sure that my working out is correct.

[Collin Li]

This describes:



By symmetry, those two terms represent the same area (the tails of the normal distribution), so one tail is just:



The complement of which is:

By symmetry around the mean:

Now we can use to find .