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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
![Confidence Interval [Simply explained]](https://i.ytimg.com/vi/ENnlSlvQHO0/mqdefault.jpg)
