When i did this before i just added the deviaition to the mean. thid doesnt work. how do i solve. is it the z score i need to find? thanks **Understanding Sampling Distributions: An Educational Overview****Concept: Sampling Distribution of Tree Heights**Let \( X \) represent the full height of a certain species of tree. Assume that \( X \) follows a normal probability distribution with a mean (\( \mu \)) of 68.2 feet and a standard deviation (\( \sigma \)) of 24 feet.**Objective:**You are planning to measure a random sample of \( n = 224 \) trees. The bell curve below illustrates the distribution of these sample means. The scale on the horizontal axis indicates the standard error of the sampling distribution.**Tasks:**1. Calculate the mean of the sample means (\( \mu_{\bar{x}} \)).2. Determine the standard error (\( \sigma_{\bar{x}} \)).**Diagram Explanation:**- **Bell Curve:** The curve represents the normal distribution of the sample means for the tree heights.- **Horizontal Axis:** Measures the standard error, which is the standard deviation of the sampling distribution of sample means.- **Boxes:** Indicate areas where calculated values should be placed, specifically the mean and standard error.**Calculated Values:**- Mean of the sample means (\( \mu_{\bar{x}} \)): 68 (shown in the filled box)- Standard error (\( \sigma_{\bar{x}} \)): 1.6 (shown in the filled box)This diagram and explanation demonstrate how to calculate and interpret the distribution of the sample means, facilitating a deeper understanding of statistical sampling in a practical context.

Given Data Population Mean,μ = 68.2 Population Standard Deviation,σ = 24.0 sample size n = 224solution : mean of the sampling distribution of the mean μ_x̄ = μ = 68.2 standard deviation of the sampling distribution of the mean σ_x̄ = σ/√n = 24.0 /√ 224 = 1.6 u - 2 *σ_x̄ = 68.2 - 2*1.6 = 65 u + 2 *σ_x̄ = 68.2 - 2*1.6 = 71.4

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Statistics

Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with mean 68.2 ft and standard deviation 24 ft. You intend to measure a random sample of n = 224 trees. The bell curve below represents the dist of these sample means. The scale on the horizontal axis is the standard error of the sampling distrib Complete the indicated boxes, correct to two decimal places. 68. V 1.6 V %3D 68. V o

Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with mean 68.2 ft and standard deviation 24 ft. You intend to measure a random sample of n = 224 trees. The bell curve below represents the dist of these sample means. The scale on the horizontal axis is the standard error of the sampling distrib Complete the indicated boxes, correct to two decimal places. 68. V 1.6 V %3D 68. V o

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Question

When i did this before i just added the deviaition to the mean. thid doesnt work. how do i solve. is it the z score i need to find? thanks

**Understanding Sampling Distributions: An Educational Overview**

**Concept: Sampling Distribution of Tree Heights**

Let \( X \) represent the full height of a certain species of tree. Assume that \( X \) follows a normal probability distribution with a mean (\( \mu \)) of 68.2 feet and a standard deviation (\( \sigma \)) of 24 feet.

**Objective:**
You are planning to measure a random sample of \( n = 224 \) trees. The bell curve below illustrates the distribution of these sample means. The scale on the horizontal axis indicates the standard error of the sampling distribution.

**Tasks:**

1. Calculate the mean of the sample means (\( \mu_{\bar{x}} \)).
2. Determine the standard error (\( \sigma_{\bar{x}} \)).

**Diagram Explanation:**

- **Bell Curve:** The curve represents the normal distribution of the sample means for the tree heights.
- **Horizontal Axis:** Measures the standard error, which is the standard deviation of the sampling distribution of sample means.
- **Boxes:** Indicate areas where calculated values should be placed, specifically the mean and standard error.

**Calculated Values:**

- Mean of the sample means (\( \mu_{\bar{x}} \)): 68 (shown in the filled box)
- Standard error (\( \sigma_{\bar{x}} \)): 1.6 (shown in the filled box)

This diagram and explanation demonstrate how to calculate and interpret the distribution of the sample means, facilitating a deeper understanding of statistical sampling in a practical context.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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