stats po itoooo

2. The following notations for a
random variable are used in our
various solutions concerning the
normal curve
P(a<z<b) probability that z-score
is between a and b
P(z>a) probability than z score is
greater than a
P(z<a) probability than z score is
less than a

3. Where a and b are z-scores
values
For example to denote the area
between z=1 and z=2 we use the
notation
P(1<z<2) = 0.1359
“the probability that the z –score
falls between z =1 and z = 2 is
0.1359”

4. Case 1 Case 2
Greater than z Less than z
At least z At most z
More than z Not more than z
To the right of z Not greater than z
Above z To the left of z
Case 3 Between Z₁ &Z₂

6. The Probability Notations Under the Normal Curve
The following mathematical notations for a random variable
are
used in various solutions concerning the normal curve.
P ( z < a ) denotes the probability that the z-score is less than
a
P ( z > a ) denotes the probability that the z-score is greater
than a
P ( a < z < b ) denotes the probability that the z-score is
between a and b
where: a and b are z-score values.
Note: It is important to correctly interpret the phrases such as:
P ( z < a ) P ( z > a ) P ( a < z < b )
less than z greater than z z is between a and b
at most z at least z
not more than z more than z
below z above z
to the left of z to the right of z

9. Example 3: Find the area between z = -1.5 and z = 2.
(Follow the given steps)
ANSWER:

14. Exercise # 1
Determine each of the following
areas and show these graphically.
1.P( -2.07 ≤ 𝑍 ≥ 2 )
2.P( Z ≥3.05)
3. P ( 1.02 ≤ Z ≤2