USING THE ZTABLE
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 looks like that in the chart.
So, our answer will be the value we look up in the chart.
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 0 to 0.79 and 0 to 1.28.
Subtracting the values from the tables
gives us the shaded piece.
*Same side
barb2right
subtract
0.39970.2852
=
0.1145
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.
From 0 all the way out is 0.5.
The table gives from 0 to 2.83.
Subtracting the two gives us the shaded area.
0.50.4977 = 0.0023
The probability (area) is 0.0023.
Ex 4)
Find the
z
value that corresponds to the given area.
From 0 to the far right is 0.5 and the table gives from z to 0.
Subtracting 0.8962 & 0.5 gives us the value
inside the table for z to 0.
0.8962 – 0.5 = 0.3962.
This is the area/probability.
We still need the zvalue.
Looking inside the table and matching it to the zvalue outside, the closest value is 1.26.
This zvalue is
on the left.
Remember the standard normal distribution is symmetric, so all we have to do is add a
negative.
zvalue = 1.26
0.75
0
0
0.79
1.28
0
2.83
0.8962
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0
1.63
–2.36
– 0.36
– 2.06
0
DETERMINING NORMAL PROBABILITIES
EX 1)
The average daily jail population in the United States is 618,319.
If the distribution is normal and
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 Spring '09
 Normal Distribution, Probability, standard normal curve

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