According to a study done by the pew Research Center, 36% of adult Americans believe that marriage is now obsolete. In a random sample of 500 adult Americans, what is the probability that more than 38% of them believe that marriage is now obsolete? This image displays a Standard Normal Distribution table, which is used in statistics to find the probability that a statistic is observed below, above, or between a certain value.### Understanding the Table- **Columns and Rows:** - The leftmost column contains the z-values ranging from -3.4 to 0.0, in increments of 0.1. - The top row, excluding the label, shows the hundredths decimal (0.00 to 0.09) to be added to the z-value from the leftmost column.- **Cell Values:** - Each cell intersection contains the probability value corresponding to the cumulative probability of a standard normal distribution for the z-value. - The value in each cell shows P(Z < z) for the specified z-value.### Example Usage:To find P(Z < -1.23):1. Find -1.2 under the z-value column.2. Move horizontally to the right to the column under 0.03.3. Locate the value 0.1093, which is P(Z < -1.23).This table is a key tool in mathematics for calculating probabilities associated with the standard normal distribution, often used in hypothesis testing and statistical inference. The image depicts a section of the standard normal distribution table, which is used in statistics to find the probabilities related to the standard normal distribution (Z-distribution). This table provides cumulative probability (P) values for specific Z-scores. The table can be read as follows:- The leftmost column lists the Z-score values ranging from 0.0 to 3.4 in increments of 0.1.- The top row lists the decimal increments from 0.00 to 0.09. To find the cumulative probability for a specific Z-score, you combine the row and column. For example:- A Z-score of 1.3 with a further decimal of 0.04 (totalling 1.34) gives a cumulative probability of 0.9099.The table is structured such that:- Light and dark blue shading alternates row-wise, likely to help in guiding the eye across long rows.- The values themselves represent cumulative probabilities from the mean of a standard normal distribution up to the given Z-score.This type of table is commonly used in statistical calculations, particularly in hypothesis testing and confidence interval estimation.

Given Information: 36% of adult Americans believe that marriage is now obsolete i.e., p=0.36 Sample size n=500 adult Americans The objective is to determine the probability that more than 38% of them believe that marriage is now obsolete. If samples size n is larger and both np and n1-p are at least 10, then the sampling distribution of sample proportions p^ is normally distributed with mean μp^=p and standard deviation σp^=p1-pn. np=5000.36=180 n1-p=5001-0.36=320 Since np≥10 and n1-p≥10, the sampling distribution of sample proportions p^ is normally distributed with mean μp^=0.36 and σp^=0.361-0.36500=0.02146625258≈0.0215 Required probability is obtained as follows: Pp^>0.38=Pp^-μp^σp^>0.38-0.360.0215=Pz>0.93=1-Pz≤0.93=1-0.8238 [Use standard normal distribution table]=0.1762 [In the given standard normal table, look for 0.9 in the first left column and .03 along the first row, the intersection of both values is 0.8238] Therefore, the probability that more than 38% of them believe that marriage is now obsolete is 0.1762

Math

Statistics

According to a study done by the pew Research Center, 36% of adult Americans believe that marriage is now obsolete. In a random sample of 500 adult Americans, what is the probability that more than 38% of them believe that marriage is now obsolete?

According to a study done by the pew Research Center, 36% of adult Americans believe that marriage is now obsolete. In a random sample of 500 adult Americans, what is the probability that more than 38% of them believe that marriage is now obsolete?

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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