Consider a population of size N = 6, 800 with a mean of μ = 165 and standard deviation of o = 28. Compute the following z-values for either the population distribution or the sampling distributions of with given sample size. Round solutions to two decimal places, if necessary. Suppose a random single observations is selected from the population. Calculate the z-value that corresponds to x = 164. Suppose a random single observations is selected from the population. Calculate the z-value that corresponds to x = 172. 2= Suppose a random sample of 75 observations is selected from the population. Calculate the z-value that corresponds to a = 172. 2= Suppose a random sample of 125 observations is selected from the population. Calculate the z-value that corresponds to 2 = 173. 2=
Consider a population of size N = 6, 800 with a mean of μ = 165 and standard deviation of o = 28. Compute the following z-values for either the population distribution or the sampling distributions of with given sample size. Round solutions to two decimal places, if necessary. Suppose a random single observations is selected from the population. Calculate the z-value that corresponds to x = 164. Suppose a random single observations is selected from the population. Calculate the z-value that corresponds to x = 172. 2= Suppose a random sample of 75 observations is selected from the population. Calculate the z-value that corresponds to a = 172. 2= Suppose a random sample of 125 observations is selected from the population. Calculate the z-value that corresponds to 2 = 173. 2=
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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![**Topic: Calculating Z-values for Population and Sample Distributions**
Consider a population of size \( N = 6,800 \) with a mean of \( \mu = 165 \) and a standard deviation of \( \sigma = 28 \).
Compute the following z-values for either the population distribution or the sampling distributions of \( \bar{x} \) with the given sample size. Round solutions to two decimal places, if necessary.
1. **Single Observation from the Population**
- Suppose a random single observation is selected from the population. Calculate the z-value that corresponds to \( x = 164 \).
\[
z =
\]
2. **Single Observation from the Population**
- Suppose a random single observation is selected from the population. Calculate the z-value that corresponds to \( x = 172 \).
\[
z =
\]
3. **Sample of 75 Observations**
- Suppose a random sample of 75 observations is selected from the population. Calculate the z-value that corresponds to \( \bar{x} = 172 \).
\[
z =
\]
4. **Sample of 125 Observations**
- Suppose a random sample of 125 observations is selected from the population. Calculate the z-value that corresponds to \( \bar{x} = 173 \).
\[
z =
\]
**Explanation of Steps to Calculate Z-values:**
To compute the z-values in different scenarios, follow these steps:
- **For single observations:**
\[
z = \frac{x - \mu}{\sigma}
\]
- **For sample means:**
\[
z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}
\]
Where:
- \( x \) = Single observation value
- \( \bar{x} \) = Sample mean
- \( \mu \) = Population mean
- \( \sigma \) = Population standard deviation
- \( n \) = Sample size
By applying these formulas, you can solve for the z-values corresponding to different observations and sample means.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc94cb5d1-997a-49d0-b0ef-9ec02bf0a187%2Fae8a0a8a-aa87-4366-b240-0e0fa990a093%2Fxahbppk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Calculating Z-values for Population and Sample Distributions**
Consider a population of size \( N = 6,800 \) with a mean of \( \mu = 165 \) and a standard deviation of \( \sigma = 28 \).
Compute the following z-values for either the population distribution or the sampling distributions of \( \bar{x} \) with the given sample size. Round solutions to two decimal places, if necessary.
1. **Single Observation from the Population**
- Suppose a random single observation is selected from the population. Calculate the z-value that corresponds to \( x = 164 \).
\[
z =
\]
2. **Single Observation from the Population**
- Suppose a random single observation is selected from the population. Calculate the z-value that corresponds to \( x = 172 \).
\[
z =
\]
3. **Sample of 75 Observations**
- Suppose a random sample of 75 observations is selected from the population. Calculate the z-value that corresponds to \( \bar{x} = 172 \).
\[
z =
\]
4. **Sample of 125 Observations**
- Suppose a random sample of 125 observations is selected from the population. Calculate the z-value that corresponds to \( \bar{x} = 173 \).
\[
z =
\]
**Explanation of Steps to Calculate Z-values:**
To compute the z-values in different scenarios, follow these steps:
- **For single observations:**
\[
z = \frac{x - \mu}{\sigma}
\]
- **For sample means:**
\[
z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}
\]
Where:
- \( x \) = Single observation value
- \( \bar{x} \) = Sample mean
- \( \mu \) = Population mean
- \( \sigma \) = Population standard deviation
- \( n \) = Sample size
By applying these formulas, you can solve for the z-values corresponding to different observations and sample means.
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