Question

For the standard normal random variable, z, find the following:

P(z > 2.45) =

P(z > -5.33) =

P(-1.33 < z < 2.45) =

P(1.33 < z < 2.45) =

Please be as detailed as possible, thank you.

Answer 1

a) P(z > 2.45) = 0.0071

We conclude that the white area = 0.9929, so:

Blue area = 1 - white area = 1 - 0.9929 = 0.0071

Last statement can be writed in math notationa as:

P ( Z>2.45 )=1?P ( Z<2.45 )=1?0.9929=0.0071

b) P ( Z>?5.33 )=P ( Z<5.33 )=1

c)

We see that P ( Z<1.33 )=0.9082 so,

P ( Z<?1.33)=1?P ( Z<1.33 )=1?0.9082=0.0918

At the end we have:

P (?1.33<Z<2.45 )=0.9011

d)

We see that P ( Z<1.33 ) = 0.9082.

At the end we have:

P (1.33<Z<2.45 ) = 0.0847