For a standard normal distribution, find: P(z < 1.15)

Answer 1

For a standard normal distribution, mu = 0 and sigma = 1 (where mu is mean and sigma is variance). So, for:

z=(x-mu)/sigma --> z=(x-0)/1 --> z=x

so x=1.15, P(z<x) = P(z<1.15) --> z = x= 1.15 --> z=1.15

So, look up z on the z-table and since z<x, then the area under the curve to the left is the area desired, so we can pull the number directly under the table since the table shows the area under the curve to the left of the z value.

Look up z=1.15 on the z-table. (Remember that z=1.15 = 1.1 + .05.) Go down the vertical side to the number 1.1, then move to the right until the number .05.

The table value of z=1.15 on the z-table is .8749, the area under the curve to the left ( and hence the probability of P(z<1.15)) is .8749.

Some books may have a letter that represents table value of z, but for generality here I just used the phrase "table value of z" where ( if the representative letter is chi) the notation chi(z) may be used to represent table value. in which case

chi(z)=chi(1.15)= .8749

To summarize quickly:

sub in mu=0 and sigma=1 and you will have z=x. Then look this number up on the table. Since P(z<x) the number can be taken directly off the table.