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in this video we're gonna focus on a

quick and simple method of finding the

z-score given the confidence level now

for those of you who want to commit this

to memory

here are some common values if you have

a 90% confidence level it corresponds to

a z value of 1.645

if you have a 95% confidence level it

corresponds to a z value of 1.96 a 98%

confidence level corresponds to a

z-score of 2.33 and a 99% confidence

level corresponds to a z-score of 2.5 75

now let's talk about how we can get

those numbers so we said that a 95%

confidence level corresponding to a

z-score of 1.96 let's talk about how we

can get that so first we need to

calculate the area under the curve to

the left and it's going to be one plus

the confidence level divided by two the

confidence level is 95% if you divide it

by a hundred you're gonna get point nine

five as a decimal so this is one point

nine five divided by two which works out

to be point nine seven five so let me

give you a visual illustration of this

let's say this is the mean this is a

positive z-score and this is our

negative z-score between a negative Z

and positive Z the area of this region

is going to be based on the conference

level which is 95% so this area is 0.95

the other 5% is covered by the area

highlighted in blue so it's divided into

two parts so two point five percent or

point zero to five will be on the right

and point zero two five will be on the

left so if we wish to get

the entire area from the left up to

positive Z it's going to be point nine

five plus point zero to five which works

out to be point nine seven five so if

you don't want to draw a picture if you

simply want to calculate that area you

could use this formula to do so it's a

quick and simple way to calculate the

area under the curve to the left and

then you could use that to get the

z-score instead of having to draw a

picture each time and determine the area

that way so here we have a positive

z-score table and as you can see it's

going to give us the area to the left so

you want to identify the z-score given

an area of 0.975 so first we need to

look for the value point 975 in the

table and here it is so notice the row

that a corresponds to we have a value

1.9 and then look for the column number

which is point zero six so when you add

those to one point nine plus point zero

six that gives you the z-score of 1.96

so that's how you could find the z-score

given the confidence level so if you

know the confidence level you can

calculate the area to the left once you

have the area to the left you could use

this table to get the corresponding

z-score now for the sake of practice

determine the z-score given a confidence

level of 97% and a confidence level of

92% so feel free to pause the video and

work on these two problems so find the

z-scores that correspond to these two

confidence levels now let's calculate

the area to the left first using this

formula

so it's one plus the confidence level

divided by two so this is going to be

0.97 for the confidence level so we have

one point nine seven divided by two

which will give us point nine eight five

now I'm going to do the other one

simultaneously as well so using the same

formula but the CL is going to be 0.92

instead of 0.9 seven and so we have one

point nine two divided by two and that's

point nine six now using a table that we

just use earlier allocate an area of

0.98 five this should give you a Z value

of 2 point 17 that's your answer for the

97 percent confidence level now using an

area of 0.96 this should give you a z

value of 1.75 so that's the area I mean

that's the Z value that corresponds to a

92 percent confidence level and I'm

going to show you that with the table

shortly so here we are back to the table

now for a 97 percent confidence level we

got an area value of 0.98 5 so we need

to locate that on the table and here it

is now this corresponds to two point one

on the left and the column is point zero

seven so we can see that for an area

value of point nine eight five this

gives us a z-score of two point one

seven if we add to point one plus point

zero seven so that was for the 97

percent confidence level now for the 92

percent confidence level and we

calculated the area to the left to be

0.96 so we got to look for point nine

six

so 0.96 were you at so this right here

is the closest we have to point nine six

point nine five nine nine four and so

that corresponds to one point seven and

then point zero five so if we add one

point seven and point zero five it gives

us a z-score of one point seven five so

that's how you could use the z-score

table to convert a confidence level into

an area and in the area value into the

z-score well the table converts the area

to the z-score you got a calculate the

area using that form I gave you earlier

so that's it for this video now you know

how to find the z-score given the

confidence level