MATLAB: An Introduction with Applications
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Suppose an x-distribution has mean μ = 8.
Consider two corresponding x distributions, the first based on samples of size n = 49 and the second based on samples of size n = 81.
(a)
What is the value of the mean of each of the two x distributions?
For n = 49, μ x =
For n = 81, μ x =
(b)
For which x distribution is P(x > 10.00) smaller? Explain your answer.
The distribution with n = 81 because the standard deviation will be larger.
The distribution with n = 49 because the standard deviation will be larger. The distribution with n = 81 because the standard deviation will be smaller.
The distribution with n = 49 because the standard deviation will be smaller.
(c)
For which x distribution is
P(6.00 < x < 10.00) greater?
Explain your answer.
The distribution with n = 49 because the standard deviation will be larger.
The distribution with n = 81 because the standard deviation will be larger. The distribution with n = 49 because the standard deviation will be smaller.
The distribution with n = 81 because the standard deviation will be smaller.
![**Understanding Sampling Distributions**
Suppose an x-distribution has a mean \(\mu = 8\). Consider two corresponding \(\bar{x}\) (sampling distribution of the sample mean) distributions. The first is based on samples of size \(n = 49\), and the second is based on samples of size \(n = 81\).
**(a) Calculating the Mean of the Sampling Distributions**
What is the value of the mean of each of the two \(\bar{x}\) distributions?
- For \(n = 49\), \(\mu_{\bar{x}} =\) [Enter Mean]
- For \(n = 81\), \(\mu_{\bar{x}} =\) [Enter Mean]
**(b) Probability that \(\bar{x}\) Exceeds a Certain Value**
For which \(\bar{x}\) distribution is \(P(\bar{x} > 10.00)\) smaller? Explain your answer.
- \( \bigcirc \) The distribution with \(n = 81\) because the standard deviation will be larger.
- \( \bigcirc \) The distribution with \(n = 49\) because the standard deviation will be larger.
- \( \bigcirc \) The distribution with \(n = 81\) because the standard deviation will be smaller.
- \( \bigcirc \) The distribution with \(n = 49\) because the standard deviation will be smaller.
**(c) Probability within a Range**
For which \(\bar{x}\) distribution is \(P(6.00 < \bar{x} < 10.00)\) greater? Explain your answer.
- \( \bigcirc \) The distribution with \(n = 49\) because the standard deviation will be larger.
- \( \bigcirc \) The distribution with \(n = 81\) because the standard deviation will be larger.
- \( \bigcirc \) The distribution with \(n = 49\) because the standard deviation will be smaller.
- \( \bigcirc \) The distribution with \(n = 81\) because the standard deviation will be smaller.
This exercise helps understand the relationship between sample size, standard deviation, and probabilities in normal distributions.](https://content.bartleby.com/qna-images/question/a4c5a3da-f5e3-4bbf-bd48-b9865949dfc0/781d52aa-5c74-47e1-9d9e-6367a2869edd/c7dcic9_processed.png)
Transcribed Image Text:**Understanding Sampling Distributions**
Suppose an x-distribution has a mean \(\mu = 8\). Consider two corresponding \(\bar{x}\) (sampling distribution of the sample mean) distributions. The first is based on samples of size \(n = 49\), and the second is based on samples of size \(n = 81\).
**(a) Calculating the Mean of the Sampling Distributions**
What is the value of the mean of each of the two \(\bar{x}\) distributions?
- For \(n = 49\), \(\mu_{\bar{x}} =\) [Enter Mean]
- For \(n = 81\), \(\mu_{\bar{x}} =\) [Enter Mean]
**(b) Probability that \(\bar{x}\) Exceeds a Certain Value**
For which \(\bar{x}\) distribution is \(P(\bar{x} > 10.00)\) smaller? Explain your answer.
- \( \bigcirc \) The distribution with \(n = 81\) because the standard deviation will be larger.
- \( \bigcirc \) The distribution with \(n = 49\) because the standard deviation will be larger.
- \( \bigcirc \) The distribution with \(n = 81\) because the standard deviation will be smaller.
- \( \bigcirc \) The distribution with \(n = 49\) because the standard deviation will be smaller.
**(c) Probability within a Range**
For which \(\bar{x}\) distribution is \(P(6.00 < \bar{x} < 10.00)\) greater? Explain your answer.
- \( \bigcirc \) The distribution with \(n = 49\) because the standard deviation will be larger.
- \( \bigcirc \) The distribution with \(n = 81\) because the standard deviation will be larger.
- \( \bigcirc \) The distribution with \(n = 49\) because the standard deviation will be smaller.
- \( \bigcirc \) The distribution with \(n = 81\) because the standard deviation will be smaller.
This exercise helps understand the relationship between sample size, standard deviation, and probabilities in normal distributions.
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