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.

Answered: Suppose an x-distribution has mean μ =…

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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.

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