Austin decided to give Taylor Swift another chance. So, he listened through all her songs from 2009. There were 8 in total. Let the random variable X be the number of songs in which she complained about some boy. The probability of complaining about a boy is 56%. *ONLY NEED HELP WITH D*a.) Is X a discrete or continuous random variable? How do you know?b.) What are the possible values of X?c.) What is the probability distribution function of X?D.) True or False? The probability that Taylor Swift complains about a boy in at least 2 songs equals the probability that Taylor Swift complains about a boy in more than 1 song? ### Standard Normal Cumulative Probability TableThis table provides cumulative probabilities for negative z-values in a standard normal distribution. The values indicate the probability that a standard normal random variable is less than or equal to a specified z-value.#### Z-values and Corresponding Probabilities:- **Z-values** are shown in the first column, ranging from -3.4 to 0.0.- The **probability values** corresponding to each z-value are shown in columns under headings that range from 0.00 to 0.09. These headings represent the second decimal place in the z-value.#### Table Entries:For example:- **For z = -3.4:** - At 0.00: 0.0003 - At 0.09: 0.0002- **For z = -1.6:** - At 0.00: 0.0548 - At 0.09: 0.0455#### Example of Usage:To find the cumulative probability of a z-value of -1.23:- Locate -1.2 in the first column.- Move across the row to the 0.03 column to find the value 0.1093.#### Graph Explanation:Above the table is a bell curve representing the standard normal distribution. The shaded area under the curve to the left of a specified z-value indicates the cumulative probability. This graphical representation helps in visualizing the proportion of the data within a given z-value range.This table is vital for statistical analyses involving standard normal distributions, including hypothesis testing and confidence interval calculations. ## Standard Normal Distribution**Equation:**\[p(z \leq z_1) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{z_1} e^{-\frac{1}{2}z^2} \, dz\]This equation represents the probability that a standard normal random variable \( z \) is less than or equal to \( z_1 \).### Diagram:- The graph at the top is a typical bell-shaped curve, representing a standard normal distribution where the mean is 0 and the standard deviation is 1. This is symmetrical about the mean, depicting the spread of probabilities across values of \( z \).### Standard Normal Distribution Table:The table provides cumulative probabilities for different \( z \)-scores, which are standardized values that map a normal distribution to a standard normal distribution.- **Columns and Rows:** - The first column (labeled \( z_1 \)) and the first row indicates \( z \)-scores. For instance, a \( z \)-score of 0.0 is in the first row and column. - The numbers are cumulative probabilities from the normal distribution up to the particular \( z \)-score.- **Highlighted Values:** - The value 0.05 is bolded for \( z = 0.0 \) and \( z = 2.0 \), showing probabilities of 0.5199 and 0.9772, respectively. - The row for \( z = 2.1 \) is highlighted, focusing on values relevant for this \( z \)-score.### Example Usage:To find the probability of a \( z \)-score less than or equal to 0.56:- Locate 0.5 in the first column.- Move across to the column under 0.06.- The probability is 0.7123.This table is crucial for assessing probabilities and percentiles in a standard normal distribution, aiding in hypothesis testing and data analysis.

Name: Austin decided to give Taylor Swift another chance. So, he listened th
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Austin decided to give Taylor Swift another chance. So, he listened through all her songs from 2009. There were 8 in total. Let the random variable X be the number of songs in which she complained about some boy. The probability of complaining about