The probability that Taylor Swift is Austin’s favorite music artist is .10. The probability that he will go to one of her concerts is .84. However, the probability that he does not like Taylor Swift and will go to a concert (because his wife makes him) is .75.Are event A and event B independent? Justify your answer numerically (be exact here!). # Standard Normal Cumulative Probability Table## IntroductionThis table provides cumulative probabilities for negative z-values under the standard normal distribution. It is used for finding the probability that a statistic is less than a given z-value.## Structure of the TableThe table is organized with z-values displayed in the leftmost column, ranging from -3.4 to 0.0. The columns to the right represent the decimals of the z-values, ranging from 0.00 to 0.09. In general, each cell in the table represents the cumulative probability for the corresponding z-value.## Graphical RepresentationOn the top right, there is a standard normal distribution curve with a shaded area representing the cumulative probability to the left of a specific z-value.## Example of UsageTo find the cumulative probability for a z-value of -2.53:- Locate -2.5 in the leftmost column.- Move across to the column labeled 0.03.- The intersection gives a cumulative probability of 0.0057.## Detailed ValuesBelow are selected cumulative probabilities for specified z-values:- **z = -3.4:** P = 0.0003- **z = -3.0:** P = 0.0013- **z = -2.5:** P = 0.0062- **z = -2.0:** P = 0.0228- **z = -1.5:** P = 0.0668- **z = -1.0:** P = 0.1587- **z = -0.5:** P = 0.3085This table is essential for statistical analysis involving the standard normal distribution, often used in hypothesis testing and confidence interval calculations. # Standard Normal DistributionThis image illustrates a standard normal distribution curve along with a z-table. ### Formula:The probability density function for the standard normal distribution is given by:\[ p(z \leq z_1) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{z_1} e^{-\frac{1}{2}z^2} \, dz \]### Z-Table Explanation:The table below the curve is a standard normal (z) table, which provides the cumulative probabilities associated with each z-score in a standard normal distribution. - **Left Column (`z_1`)**: This column lists the z-scores from 0.0 to 3.9, incrementing by 0.1.- **Row & Columns (0.00 to 0.09)**: These represent the hundredths place of the z-score.### How to Read the Table:1. Locate the decimal value of the z-score (e.g., 2.1).2. Move across to the column reflecting the hundredths value (e.g., 0.03).3. The intersection gives the cumulative probability. For z = 2.13, the probability is 0.9834 (highlighted).The highlighted rows and columns demonstrate notable cumulative probabilities at specific z-scores. For example:- z = 0.05 corresponds to a probability of approximately 0.5199.- z = 2.1 corresponds to a probability of approximately 0.9830.This table serves as an essential tool for statistical calculations in determining the likelihood that a standard normal random variable is less than or equal to a given z-score.

Name: The probability that Taylor Swift is Austin’s favorite music artist is
Uploaded: 2024-03-20T07:07:50.000Z
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Description: The probability that Taylor Swift is Austin’s favorite music artist is .10. The probability that he will go to one of her concerts is .84. However, the probability that he does not like Taylor Swift and will go to a concert (because his wife makes hi