Find zα/2 for α=0.14.
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
Find zα/2 for α=0.14.
![The image displays a segment of the standard normal distribution table, often used in statistics to find the probability that a statistic is observed below a certain value (known as the z-score) in a standard normal distribution.
### Diagram Explanation
At the top, there is a bell-shaped curve, representing the normal distribution graph. The shaded area under the curve highlights a section, which corresponds to the probability associated with a specific z-score value. The horizontal axis is marked with the label "z", identifying the z-score.
### Table Explanation
The table below the graph shows a portion of z-score values and their corresponding cumulative probabilities.
- The leftmost column lists z-scores from 0.0 to 1.1, increasing in increments of 0.1.
- The top row lists decimal increments from 0.00 to 0.09.
- The intersecting cells contain the cumulative probability values.
#### Example
To find the cumulative probability for a z-score of 0.54:
- Locate 0.5 in the leftmost column.
- Move across the row to the column marked .04.
- The cumulative probability from the table is 0.2054.
This table is an essential tool for statistical analysis, allowing researchers to determine the likelihood that a data point lies below a given z-score within a normal distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b6f6898-f27b-4fa8-a9b3-0dfd3a3fd80e%2Fef14277f-2541-4d7e-a239-f81d738b7032%2F3oxdtxt_processed.jpeg&w=3840&q=75)
![The image displays a z-table, which is used in statistics to find the probability of a statistic falling below a particular z-score in a standard normal distribution. The table lists z-scores in the first column and corresponding probabilities in the remaining columns.
### Explanation of the Table:
- **Rows and Columns:**
- The leftmost column shows the integer and first decimal of z-scores (from 1.1 to 3.0).
- The top row shows the second decimal place of z-scores (from 0 to 0.09).
- **How to Use the Table:**
- To find the probability for a z-score, locate the first part of the z-score in the left column. For example, for a z-score of 1.23, find 1.2 in the first column.
- Next, locate the second decimal in the top row (0.03 for 1.23).
- Find the intersection of the row and column, which gives the probability (0.3917 for a z-score of 1.23).
This table helps determine the cumulative probability of a z-score being below a given value in a standard normal distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b6f6898-f27b-4fa8-a9b3-0dfd3a3fd80e%2Fef14277f-2541-4d7e-a239-f81d738b7032%2F3bxwet_processed.jpeg&w=3840&q=75)
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