et x be a continuous random variable that has a normal distribution with μ = 48 and robability that the sample mean, x, for a random sample of 16 taken from this populat Round your answer to four decimal places. (x > 44.90) = i
et x be a continuous random variable that has a normal distribution with μ = 48 and robability that the sample mean, x, for a random sample of 16 taken from this populat Round your answer to four decimal places. (x > 44.90) = i
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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![**Problem Statement:**
Let \( x \) be a continuous random variable that has a normal distribution with \( \mu = 48 \) and \( \sigma = 8 \). Assuming \( \frac{n}{N} \leq 0.05 \), find the probability that the sample mean, \( \bar{x} \), for a random sample of 16 taken from this population will be more than 44.90.
Round your answer to four decimal places.
\[ P(\bar{x} > 44.90) = \] [Input Box]
---
**Explanation:**
1. **Parameters Given:**
- Population Mean (\( \mu \)): 48
- Population Standard Deviation (\( \sigma \)): 8
- Sample Size (\( n \)): 16
- Sample Mean (\( \bar{x} \)): 44.90
- Finite Population Correction Factor (Assuming \( \frac{n}{N} \leq 0.05 \))
2. **Goal:**
- To determine the probability that the sample mean \( \bar{x} \) for a random sample of 16 is greater than 44.90.
3. **Steps to Follow:**
- Calculate the standard error of the mean (SEM), which will be \( \frac{\sigma}{\sqrt{n}} \).
- Convert the sample mean to a z-score using \( Z = \frac{\bar{x} - \mu}{SEM} \).
- Use the z-score to find the corresponding probability from the standard normal distribution.
4. **Notes:**
- Round the final answer to four decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcce67d60-ba9c-4b65-a73f-671ae19935ed%2F172c483a-669c-4023-a790-de3c396b9a06%2F6ju0je_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Let \( x \) be a continuous random variable that has a normal distribution with \( \mu = 48 \) and \( \sigma = 8 \). Assuming \( \frac{n}{N} \leq 0.05 \), find the probability that the sample mean, \( \bar{x} \), for a random sample of 16 taken from this population will be more than 44.90.
Round your answer to four decimal places.
\[ P(\bar{x} > 44.90) = \] [Input Box]
---
**Explanation:**
1. **Parameters Given:**
- Population Mean (\( \mu \)): 48
- Population Standard Deviation (\( \sigma \)): 8
- Sample Size (\( n \)): 16
- Sample Mean (\( \bar{x} \)): 44.90
- Finite Population Correction Factor (Assuming \( \frac{n}{N} \leq 0.05 \))
2. **Goal:**
- To determine the probability that the sample mean \( \bar{x} \) for a random sample of 16 is greater than 44.90.
3. **Steps to Follow:**
- Calculate the standard error of the mean (SEM), which will be \( \frac{\sigma}{\sqrt{n}} \).
- Convert the sample mean to a z-score using \( Z = \frac{\bar{x} - \mu}{SEM} \).
- Use the z-score to find the corresponding probability from the standard normal distribution.
4. **Notes:**
- Round the final answer to four decimal places.
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