Consider the following exercises regarding probability (hint: draw some Venn Diagrams)The P(A) = .36 and the P(B) = .64. Give a range [min, max] inclusive of possible values that P(A ⋂ B) can take. Can we have the case where P(A) = .65, P(A ⋃ B)= .60, and P(B) = .14? Explain your answer **Standard Normal Cumulative Probability Table**This table provides cumulative probabilities for negative z-values. It is used to find the probability that a standard normal random variable is less than a given z-value. The table displays a range of z-values from -3.4 to 0.0, with columns labeled 0.00 to 0.09 representing the hundredths place.At the top right of the table, there is a diagram of a standard normal distribution curve with the shaded area representing the cumulative probability from the left up to the specified z-score.**Table Explanation:**- **Rows:** Each row represents a primary z-value (e.g., -3.4, -3.3, ..., -0.5).- **Columns:** Each column, starting from 0.00 to 0.09, provides the added decimal to the main z-value from the row header. The intersection gives the cumulative probability.**Example of Usage:**- For a z-value of -2.5: - Locate the row for -2.5. - Move across to the desired column. For instance, for -2.56, use column 0.06, which corresponds to a cumulative probability of 0.0052.This table is integral in statistics for calculating probabilities and understanding distributions within a standard normal model. **Standard Normal Distribution Table**The image illustrates a standard normal distribution table used to find probabilities associated with the standard normal distribution, often used in statistics for data analysis.### Components of the Image:1. **Graph of Standard Normal Distribution:** - The bell-shaped curve depicted at the top of the image represents the standard normal distribution. The shaded area under the curve to the left of \( z_1 \) symbolizes the cumulative probability of obtaining a value less than or equal to a specific \( z \)-score.2. **Probability Density Function (PDF):** - The formula for calculating cumulative probabilities is given by: \[ p(z \leq z_1) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{z_1} e^{-\frac{1}{2}z^2} \, dz \] - This equation defines the probability that a value from a standard normal distribution is less than or equal to \( z_1 \).3. **Standard Normal Distribution Table:** - **Rows and Columns:** The table lists \( z \)-scores to two decimal places. The row headers (e.g., 0.0, 0.1, ..., 3.9) represent the whole and first decimal place of a \( z \)-score, while the column headers (0.00 to 0.09) represent the second decimal place. - **Values:** Each cell in the table contains the cumulative probability associated with the \( z \)-score formed by combining the row and column headers. For example, to find the cumulative probability up to a \( z \)-score of 0.05, locate the row for 0.0 and column for 0.05; the cell shows 0.5199, highlighted in green. - **Highlighted Cells:** Some cells, such as 0.05 (0.5199) and 2.10 (0.9830), are highlighted to aid identification of key probabilities.The table provides a useful reference for determining cumulative probabilities related to the standard normal distribution, crucial for statistical analysis and hypothesis testing.

Name: Consider the following exercises regarding probability (hint: draw som
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Consider the following exercises regarding probability (hint: draw some Venn Diagrams)The P(A) = .36 and the P(B) = .64. Give a range [min, max] inclusive of possible values that P(A ⋂ B) can take. Can we have the case where P(A) = .65, P(A ⋃ B)= .60