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USING THE Z-TABLE
Ex.
1)
Find the area under the normal distribution curve.
Between z=0 and z=0.75
Start by drawing the standard normal curve and shading the desired area.
The shaded area does not look like that in the chart.
The chart will give from negative infinity (the left) to 0 and
from negative infinity(the left) to 0.75.
We can subtract the
two areas/probabilities to determine the answer.
0.7734 – 0.5 = 0.2734
The area (probability) is 0.2734
Ex 2)
Find the area under the standard normal curve between z=0.79 and z=1.28.
Start by drawing the standard normal curve and shading the desired area.
The table gives negative infinity to
0.79 and negative infinity to 1
Subtracting the values from the tables
gives us the shaded piece.
.28.
in.)
0.8997 – 0.7852 = 0.1145
(If you subtract in the wrong order, the
answer will be negative.
Just switch
the values and subtract aga
Area/probability 0.1145
Ex. 3)
Find the probability.
P( z > 2.83)
Start by drawing the standard normal curve and shading the desired area.
The chart gives from negative infinity to 2.83. The total
area/probability must equal 1.
So, we can subtract 1 from the
value we obtain in the chart.
1-0.9977 = 0.0023
Or we can use symmetry to determine the answer.
Because of symmetry, this is the same as asking for negative
infinity to -2.83.
That would then look like the left-side of the
charts (see the picture at the bottom of the chart).
Once we look
up -2.83, then we are done.
We do not change the 0.0023 that
we are obtaining from the chart because probabilities are always positive.
The probability (area) is 0.0023.
Ex 4)
Find the
z
value that corresponds to the given area.
0.75
0
0
0.79
1.28
0
2.83
0.8962

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The left chart gives the non-shaded area.
Our total probability must add up to 1.
So, 1-0.8962 = 0.1038
would have been the value we would have obtained from the inside of the chart.
Matching it up to it’s
corresponding z-value of -1.26.
OR.

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