Find the z-scores for which 28% of the distribution's area lies between −z and z. The image shows a Standard Normal Distribution Table (Page 2), which is used to find the cumulative probability associated with a standard normal random variable \(Z\). This table displays the probabilities for \(z\)-scores ranging from 0.0 to 2.1 across the top, arranged in increments of 0.01.**Description of the Table Layout:**- **Rows:** Correspond to the first decimal place of the \(z\)-score.- **Columns:** Correspond to the second decimal place of the \(z\)-score.- **Values:** Each cell intersection displays the cumulative probability \(P(Z \leq z)\) for the corresponding \(z\)-score.**Example for Clarity:**- For \(z = 0.25\): - Identify the row for 0.2. - Locate the column for 0.05. - The probability at the intersection is \(0.5987\), meaning the probability that a standard normal variable \(Z\) is less than or equal to 0.25 is 0.5987.**Additional Usage Tips:**- To find the probability that \(Z\) is greater than a particular \(z\)-score, subtract the table value from 1.- This table aids in statistical analysis, particularly in hypothesis testing and confidence interval estimation.This comprehensive layout ensures that users can easily lookup and understand probabilities associated with various \(z\)-scores in the context of normal distribution. ## Standard Normal Table (Page 1)This Standard Normal Table lists cumulative probabilities corresponding to z-scores in a standard normal distribution. Each row represents a z-score value, and each column represents the hundredths decimal to be added to the z-score in the leftmost column. The table entries represent the area (probability) to the left of the specified z-score.### Table Breakdown- **Columns**: Each column heading (.09 to .00) represents incremental changes from the main z-score in tenths.- **Rows**: Each row begins with a z-score (ranging from -3.4 to -1.3).- **Intersection values**: Each cell shows the cumulative probability corresponding to the z-score plus the hundredths value from the column header.### Usage ExampleTo find the cumulative probability for a z-score of -2.57:1. Locate the row for z = -2.5.2. Find the column for .07.3. The intersecting value (0.0051) represents the cumulative probability that a standard normal random variable will be less than -2.57.### Table EntriesThe entries are values like:- **z = -3.4:** Starts from 0.0002 in column .09 and goes to 0.0003 at column .00.- **z = -3.3:** Starts from 0.0003 in column .09 and goes to 0.0005 at column .00.- And so on up to,- **z = -1.3:** Starts from 0.0823 in column .09 and goes to 0.0968 at column .00.This table is crucial for those studying statistics as it helps in determining probabilities and can be used in various statistical analyses, specifically Z-tests and hypothesis testing.

Here, the z score for which 28% of thedistribution's area lies between minus−z and z where the z-scores asymptotically follows standard normal distribution. P(-z≤Z≤z) = 0.28 =>P(Z≤z) - P(Z≤-z) = 0.28 => P(Z≤z) -[1-P(Z≤z)] = 0.28 => P(Z≤z) = (1+0.28)/2 = 0.64 => z = 0.3585 So the required z-scores will be (-0.3585, 0.3585)

Answered: Find the z-scores for which 28% of…

Math

Statistics

Find the z-scores for which 28% of the distribution's area lies between −z and z.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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