We can solve the area above the z score of
1.46 by using the Z Table or by using a Casio
fx-570es PLUS calculator. You will be shown
two methods in solving the area above the z
score 1.46.
Methods In Solving The Area Under the
Curve 1. Manual process using the Z-Table
2. Using Scientific Calculator (Casio fx-570es PLUS)
The area under the normal curve is. approximately 100% or 1, thus, half of it is 50%
or 0.50. The z score given is a positive value
then it's located in right region of the graph.
Properties of The Normal Curve
1. Its area is 1.
2. It symmetric with respect to the measures
of central tendency (mean, median and
mode)
3. The curve is bell-shaped,
4. The curve's width is determined by the
number of standard deviations of the
distribution.
Manual Process:
Refer to the graph below. The shaded region
Is the desired area that needs to be solved. It is to the right of the z-score 1.46 because the problem is asking above the mentioned z score.
Using the Z-table, on the very first column
look for the z score 1.4 and on the very first
row find the z-score 0.06, the reason why we
choose the z scores 1.4 and 0.06 is when we
add these two values, the result is 1.46 which
is the actual given z-score. The value where
the two z-scores (1.40 and 0.06) intersect is
the area on the graph from z score 0 to 1.46
or the white region from the middle line to
1.46.
To solve for the shaded or desired area,
subtract 0.4279 from 0.5000 (because half of
the graph's area is 0.5000).
0.5000 0.4279-0.07210.5000-0.4279-0.0721
Thus, the area above the z score of 1.46 is
0.0721.
Using Scientific Calculator (Casio fx-570es
PLUS):
1. Press Mode
2. Choose STAT (option 3)
3. Press AC (It should clear the screen.)
4. Press Shift+1
5. Choose Distr (Stands for Distribution)
(Option 5)
6. Choose the command R(
7. Then, plug in the z-score (1.46)
8. Hit Equal
The calculator should show the value
0.072145\approx(0.072130.072145-0.0721.
