Question

Find the area under the normal distribution curve between z = 1.30 and z = 3.25.

Answer 1

which option do you want to use: table or calculator?

Answer 2

table

Answer 3

ok we can use a table like this one

https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf

Answer 4

does something like that look familiar?

Answer 5

Yes Thanks I'm kind of confused with this lesson

Answer 6

first we'll find P(Z < 1.30)

look at the row that starts with `1.3`
then find the column that has `.00` at the top of the column
what number is at the intersection of that row and column?

Answer 7

.90320

Answer 8

good

Answer 9

do the same for P(Z < 3.25)

Answer 10

look at the row starting with `3.2`
and the column starting with `0.05`

Answer 11

.99942

Answer 12

now subtract the two (bigger - smaller)

Answer 13

wow Thanks a lot. That's an answer choice I appreciate it

Answer 14

you should get .99942-.90320 = 0.09622

so P(1.30 < z < 3.25) = 0.09622

The rule I used was

\[\Large P({\color{red}{a}} < z < {\color{blue}{b}}) = P(z < {\color{blue}{b}}) - P(z < {\color{red}{a}})\]
where b > a
so,

\[\Large P({\color{red}{1.30}} < z < {\color{blue}{3.25}}) = P(z < {\color{blue}{3.25}}) - P(z < {\color{red}{1.30}})\]