A simple random sample of size n=40 is obtained from a population with a mean of 20 and a standard deviation of 5. Is the sampling distribution normally distributed? Why? O Yes, the sampling distribution is normally distributed because the sample size is greater than 30. Yes, the sampling distribution is normally distributed because the population is normally distributed. No, the sampling distribution is not normally distributed because the population is not normally distributed. No, the sampling distribution is not normally distributed because the population mean is less than 30.
A simple random sample of size n=40 is obtained from a population with a mean of 20 and a standard deviation of 5. Is the sampling distribution normally distributed? Why? O Yes, the sampling distribution is normally distributed because the sample size is greater than 30. Yes, the sampling distribution is normally distributed because the population is normally distributed. No, the sampling distribution is not normally distributed because the population is not normally distributed. No, the sampling distribution is not normally distributed because the population mean is less than 30.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![**Understanding Sampling Distribution**
**Question:**
A simple random sample of size n=40 is obtained from a population with a mean of 20 and a standard deviation of 5. Is the sampling distribution normally distributed? Why?
**Answers:**
1. **[ ] Yes, the sampling distribution is normally distributed because the sample size is greater than 30.**
2. **[ ] Yes, the sampling distribution is normally distributed because the population is normally distributed.**
3. **[ ] No, the sampling distribution is not normally distributed because the population is not normally distributed.**
4. **[ ] No, the sampling distribution is not normally distributed because the population mean is less than 30.**
**Explanation:**
For this question, the concept of the Central Limit Theorem (CLT) is pivotal. According to the CLT, regardless of the population's distribution, the sampling distribution of the sample mean will tend to be normally distributed if the sample size is sufficiently large (typically n > 30). Given that the sample size here is 40, which is greater than 30, this criterion is met.
Thus, the most accurate answer would be:
**1. Yes, the sampling distribution is normally distributed because the sample size is greater than 30.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F828fe599-f033-4e13-bbc5-938fe3ceb9f0%2F9dd44f3c-24d4-4e7a-8b21-bfdbb4e50575%2Flpcfbwq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Sampling Distribution**
**Question:**
A simple random sample of size n=40 is obtained from a population with a mean of 20 and a standard deviation of 5. Is the sampling distribution normally distributed? Why?
**Answers:**
1. **[ ] Yes, the sampling distribution is normally distributed because the sample size is greater than 30.**
2. **[ ] Yes, the sampling distribution is normally distributed because the population is normally distributed.**
3. **[ ] No, the sampling distribution is not normally distributed because the population is not normally distributed.**
4. **[ ] No, the sampling distribution is not normally distributed because the population mean is less than 30.**
**Explanation:**
For this question, the concept of the Central Limit Theorem (CLT) is pivotal. According to the CLT, regardless of the population's distribution, the sampling distribution of the sample mean will tend to be normally distributed if the sample size is sufficiently large (typically n > 30). Given that the sample size here is 40, which is greater than 30, this criterion is met.
Thus, the most accurate answer would be:
**1. Yes, the sampling distribution is normally distributed because the sample size is greater than 30.**
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