To determine the areas and show them graphically, we will use the standard normal distribution table and the properties of the normal distribution.
1. Area above z = 1.54:
Using the standard normal distribution table, we can find that the area to the right of z = 1.54 is 0.0618. Therefore, the area above z = 1.54 is 0.0618.
Graphically, this can be represented as follows:
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|__|_______
1.54
Area below z = -1.7:
2. Using the standard normal distribution table, we can find that the area to the left of z = -1.7 is 0.0446. Therefore, the area below z = -1.7 is 0.0446.
Graphically, this can be represented as follows:
|__|_______
-1.7
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---- |
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3. Area between z = 0.83 and z = 2.30:
Using the standard normal distribution table, we can find the areas to the left of z = 0.83 and z = 2.30, which are 0.7967 and 0.9893, respectively. Therefore, the area between z = 0.83 and z = 2.30 is the difference between these two areas: 0.9893 - 0.7967 = 0.1926.
Graphically, this can be represented as follows:
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|____|__________
0.83 2.30
4. Area at most z = 0.93:
The area at most z = 0.93 is the area to the left of z = 0.93. Using the standard normal distribution table, we can find that this area is 0.8238.
Graphically, this can be represented as follows:
|____|__________
0.93
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5. Area between z = -1.24 and z = 1.81:
Using the standard normal distribution table, we can find the areas to the left of z = -1.24 and z = 1.81, which are 0.1075 and 0.9649, respectively. Therefore, the area between z = -1.24 and z = 1.81 is the difference between these two areas: 0.9649 - 0.1075 = 0.8574.
Answers & Comments
To determine the areas and show them graphically, we will use the standard normal distribution table and the properties of the normal distribution.
1. Area above z = 1.54:
Using the standard normal distribution table, we can find that the area to the right of z = 1.54 is 0.0618. Therefore, the area above z = 1.54 is 0.0618.
Graphically, this can be represented as follows:
/|
/ |
/ |
---- |
| |
| |
| |
| |
| |
| |
|__|_______
1.54
Area below z = -1.7:
2. Using the standard normal distribution table, we can find that the area to the left of z = -1.7 is 0.0446. Therefore, the area below z = -1.7 is 0.0446.
Graphically, this can be represented as follows:
|__|_______
-1.7
| |
| |
| |
| |
| |
---- |
\ |
\ |
\|
3. Area between z = 0.83 and z = 2.30:
Using the standard normal distribution table, we can find the areas to the left of z = 0.83 and z = 2.30, which are 0.7967 and 0.9893, respectively. Therefore, the area between z = 0.83 and z = 2.30 is the difference between these two areas: 0.9893 - 0.7967 = 0.1926.
Graphically, this can be represented as follows:
/|
/ |
/ |
______/ |
| |
| |
| |
| |
| |
| |
|____|__________
0.83 2.30
4. Area at most z = 0.93:
The area at most z = 0.93 is the area to the left of z = 0.93. Using the standard normal distribution table, we can find that this area is 0.8238.
Graphically, this can be represented as follows:
|____|__________
0.93
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------ |
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|__|
5. Area between z = -1.24 and z = 1.81:
Using the standard normal distribution table, we can find the areas to the left of z = -1.24 and z = 1.81, which are 0.1075 and 0.9649, respectively. Therefore, the area between z = -1.24 and z = 1.81 is the difference between these two areas: 0.9649 - 0.1075 = 0.8574.
Graphically, this can be represented as follows:
|____|_____________________
-1.24 1.81
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