In a population where 76 % of voters prefer Candidate A, how many voters must be sampled for the distribution of voters that prefer candidate A to be normally distributed?
In a population where 76 % of voters prefer Candidate A, how many voters must be sampled for the distribution of voters that prefer candidate A to be normally distributed?
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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![**Question:**
In a population where 76% of voters prefer Candidate A, how many voters must be sampled for the distribution of voters that prefer Candidate A to be normally distributed?
**[Answer Box]**
*Note: To determine the sample size required for the sampling distribution to be approximately normal, you can use the Central Limit Theorem. Generally, a sample size of at least 30 is considered sufficient for most distributions, but for proportions, you may use the rule of thumb that both np and n(1-p) should be greater than 5, where n is the sample size and p is the proportion.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F020b4ff6-36e2-475f-88e0-c8be863ccb7d%2F8905a8df-4c5f-4a7f-85eb-4c466f09ad1c%2Fg6t1mid_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
In a population where 76% of voters prefer Candidate A, how many voters must be sampled for the distribution of voters that prefer Candidate A to be normally distributed?
**[Answer Box]**
*Note: To determine the sample size required for the sampling distribution to be approximately normal, you can use the Central Limit Theorem. Generally, a sample size of at least 30 is considered sufficient for most distributions, but for proportions, you may use the rule of thumb that both np and n(1-p) should be greater than 5, where n is the sample size and p is the proportion.*
Expert Solution

Step 1
The sampling distribution of the sample proportion is approximately normal with at least 5 expected successes and 5expected failures. To find whether the distribution is normal, multiply the trials n by p and by (1-p).
Given:
p = 0.76
Now,
n(1-p) = 5
n * (1-0.76)= 5
n =20.833
n =21
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