Question

Find the standard normal area for each of the following (Round your answers to 4 decimal places.): Standard normal area a. P( Z ≤ 2.16) b. P(Z ≤ 3.05) c. P(Z ≤ 2.05) d. P(Z > 0.55)

Answer 1

You can use excel or standard normal table

Using Excel

Method 1 : select any cell and in the fx option above type " =NORM.S.DIST(2.16,TRUE) " this will give value Z<=2.16

you can edit formulae for any given x such that you have to find Z<=x by "=NORM.S.DIST(x,TRUE)"

For normal distribution P(Z>=x) is equal to 1-P(Z<=x) so formula get modified to

"=1-NORM.S.DIST(x,TRUE)"

but it can be hard to remember this every time

So you can use method 2

Go to Formulas

Select more functions from there select statistical

Scroll down to find normal S. distribution select and enter the desired Z value and in cumulative option enter " TRUE".

There is no shortcut for the second type either manually subtract the answer obtained from the Normal distribution from 1 or change the formulae as mentioned above

Looking into the table is a very easy task table are available with the heading

STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score.

and this area gives you nothing but the probability of Z<=x table maximum of the table has a limitation of two decimal points.

search for 2.1 on the left-hand side of the table and then in that row go for the column with heading 0.06 there you reach 2.16 value written there is your required answer

for Z>=x see the value for Z<=x in the table and subtract it from 1.

Now answer to your problems

P(Z<=2.16) = 0.9846

P(Z<=3.05) = 0.9989

P(Z<=2.05) = 0.9798

P(Z>0.55)= 1- P(Z<=0.55)=1-0.70884=0.29116=0.2912

If you need any further clarification regarding this problem feel free to comment below