To find the areas under the standard normal curve we follow these steps:
### Part 1: Area to the right of a [tex]\( z \)[/tex]-score of 1.39
1. Locate the [tex]\( z \)[/tex]-score in the table:
- The row for [tex]\( z = 1.3 \)[/tex] and column for [tex]\( 0.09 \)[/tex] together provide the [tex]\( z \)[/tex]-score of 1.39.
- Cross-referencing these, we find that the cumulative area to the left of [tex]\( z = 1.39 \)[/tex] is [tex]\( 0.9177 \)[/tex].
2. Calculate the area to the right:
- Since the total area under the curve is 1, the area to the right of [tex]\( z = 1.39 \)[/tex] is calculated as:
[tex]\[
\text{Area to the right} = 1 - \text{Area to the left}
\][/tex]
- Substituting the known value:
[tex]\[
\text{Area to the right of } 1.39 = 1 - 0.9177 = 0.0823
\][/tex]
### Part 2: Area to the left of a [tex]\( z \)[/tex]-score of 1.53
1. Locate the [tex]\( z \)[/tex]-score in the table:
- The row for [tex]\( z = 1.5 \)[/tex] and column for [tex]\( 0.03 \)[/tex] together provide the [tex]\( z \)[/tex]-score of 1.53.
- Cross-referencing these, we find that the cumulative area to the left of [tex]\( z = 1.53 \)[/tex] is [tex]\( 0.9370 \)[/tex].
2. Area to the left of [tex]\( z \)[/tex]-score 1.53:
- The area to the left is directly given by the table value:
[tex]\[
\text{Area to the left of } 1.53 = 0.9370
\][/tex]
Based on the detailed tabulated values and the step-by-step procedure:
- The area to the right of the [tex]\( z \)[/tex]-score 1.39 is approximately [tex]\( 0.0823 \)[/tex].
- The area to the left of the [tex]\( z \)[/tex]-score 1.53 is approximately [tex]\( 0.9370 \)[/tex].
For precision, the areas derived are:
[tex]\[
\boxed{0.08226443867766897}
\][/tex]
[tex]\[
\boxed{0.9369916355360216}
\][/tex]
