having a mean equal to 21 and a standard deviation equal to 8. (a) Describe the shape of the sampling distribution of the sample mean x . Do we need to make any assumptions about the shape of the population? Why or why not? Normally distributed because the sample size is large (b)Find the mean and the standard deviation of the sampling distribution of the sample mean x. (Round your answer to 1 decimal place.) O no
having a mean equal to 21 and a standard deviation equal to 8. (a) Describe the shape of the sampling distribution of the sample mean x . Do we need to make any assumptions about the shape of the population? Why or why not? Normally distributed because the sample size is large (b)Find the mean and the standard deviation of the sampling distribution of the sample mean x. (Round your answer to 1 decimal place.) O no
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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![**Suppose that we will randomly select a sample of 79 measurements from a population having a mean equal to 21 and a standard deviation equal to 8.**
**(a) Describe the shape of the sampling distribution of the sample mean \(\bar{x}\). Do we need to make any assumptions about the shape of the population? Why or why not?**
- Normally distributed ✔️; no ✔️, because the sample size is large ✔️.
**(b) Find the mean and the standard deviation of the sampling distribution of the sample mean \(\bar{x}\). (Round your \(\sigma_{\bar{x}}\) answer to 1 decimal place.)**
- \(\mu_{\bar{x}}\) [Input Box]
- \(\sigma_{\bar{x}}\) [Input Box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F143cb558-5c1f-4ecb-a57c-3318134e8311%2F63823afd-9be3-4948-9035-0c3d6344e3ce%2Foail7v_processed.png&w=3840&q=75)
Transcribed Image Text:**Suppose that we will randomly select a sample of 79 measurements from a population having a mean equal to 21 and a standard deviation equal to 8.**
**(a) Describe the shape of the sampling distribution of the sample mean \(\bar{x}\). Do we need to make any assumptions about the shape of the population? Why or why not?**
- Normally distributed ✔️; no ✔️, because the sample size is large ✔️.
**(b) Find the mean and the standard deviation of the sampling distribution of the sample mean \(\bar{x}\). (Round your \(\sigma_{\bar{x}}\) answer to 1 decimal place.)**
- \(\mu_{\bar{x}}\) [Input Box]
- \(\sigma_{\bar{x}}\) [Input Box]
Expert Solution
Step 1
Given that.
X~N( μ , ?)
μ=21 , ?=8 , n=79
Step by step
Solved in 3 steps
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
![Suppose that we will randomly select a sample of 79 measurements from a population having a mean equal to 21 and a standard deviation equal to 8.
**(a)** Describe the shape of the sampling distribution of the sample mean \( \bar{x} \). Do we need to make any assumptions about the shape of the population? Why or why not?
- **Answer:** Normally distributed; no, because the sample size is large.
**(b)** Find the mean and the standard deviation of the sampling distribution of the sample mean \( \bar{x} \). *(Round your \( \sigma_{\bar{x}} \) answer to 1 decimal place.)*
- \( \mu_{\bar{x}} = 21 \)
- \( \sigma_{\bar{x}} = 0.9 \)
**(c)** Calculate the probability that we will obtain a sample mean greater than 23; that is, calculate \( P(\bar{x} > 23) \). Hint: Find the z value corresponding to 23 by using \( \mu_{\bar{x}} \) and \( \sigma_{\bar{x}} \) because we wish to calculate a probability about \( \bar{x} \). *(Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round z-scores to 2 decimal places.)*
- \( P(\bar{x} > 23) = \) [input box]
**(d)** Calculate the probability that we will obtain a sample mean less than 20.487; that is, calculate \( P(\bar{x} < 20.487) \). *(Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round z-scores to 2 decimal places.)*
- \( P(\bar{x} < 20.487) = \) [input box]](https://content.bartleby.com/qna-images/question/143cb558-5c1f-4ecb-a57c-3318134e8311/48ec69f7-eb7c-43fd-9012-30feb8303d46/3zzr5p7_processed.png)
Transcribed Image Text:Suppose that we will randomly select a sample of 79 measurements from a population having a mean equal to 21 and a standard deviation equal to 8.
**(a)** Describe the shape of the sampling distribution of the sample mean \( \bar{x} \). Do we need to make any assumptions about the shape of the population? Why or why not?
- **Answer:** Normally distributed; no, because the sample size is large.
**(b)** Find the mean and the standard deviation of the sampling distribution of the sample mean \( \bar{x} \). *(Round your \( \sigma_{\bar{x}} \) answer to 1 decimal place.)*
- \( \mu_{\bar{x}} = 21 \)
- \( \sigma_{\bar{x}} = 0.9 \)
**(c)** Calculate the probability that we will obtain a sample mean greater than 23; that is, calculate \( P(\bar{x} > 23) \). Hint: Find the z value corresponding to 23 by using \( \mu_{\bar{x}} \) and \( \sigma_{\bar{x}} \) because we wish to calculate a probability about \( \bar{x} \). *(Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round z-scores to 2 decimal places.)*
- \( P(\bar{x} > 23) = \) [input box]
**(d)** Calculate the probability that we will obtain a sample mean less than 20.487; that is, calculate \( P(\bar{x} < 20.487) \). *(Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round z-scores to 2 decimal places.)*
- \( P(\bar{x} < 20.487) = \) [input box]
Solution
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