18. The weight of a full-term newborn baby follows a normal distribution with a mean weight of 7.5 pounds and a standard deviation of 1.8 pounds. Find the probability that the mean weight of a sample of 20 full-term newborn babies is less than 8.6 pounds. SHOW WORK and round your answer to 4-decimal places or answer as a precent with 1-digit value.
18. The weight of a full-term newborn baby follows a normal distribution with a mean weight of 7.5 pounds and a standard deviation of 1.8 pounds. Find the probability that the mean weight of a sample of 20 full-term newborn babies is less than 8.6 pounds. SHOW WORK and round your answer to 4-decimal places or answer as a precent with 1-digit value.
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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18.
![**Question 18:**
The weight of a full-term newborn baby follows a normal distribution with a mean weight of 7.5 pounds and a standard deviation of 1.8 pounds. Find the probability that the mean weight of a sample of 20 full-term newborn babies is less than 8.6 pounds. **SHOW WORK** and round your answer to 4-decimal places or answer as a percent with a 1-digit value.
---
**Solution Explanation:**
1. **Identify the Parameters:**
- Population mean (\(\mu\)) = 7.5 pounds
- Population standard deviation (\(\sigma\)) = 1.8 pounds
- Sample size (\(n\)) = 20
2. **Calculate the Standard Error (SE):**
\[
SE = \frac{\sigma}{\sqrt{n}} = \frac{1.8}{\sqrt{20}}
\]
3. **Find the Z-score:**
- We want the probability that the sample mean is less than 8.6 pounds.
- Compute the Z-score using:
\[
Z = \frac{\bar{X} - \mu}{SE} = \frac{8.6 - 7.5}{SE}
\]
4. **Use the Z-table:**
- Look up the computed Z-score in the standard normal distribution table to find the probability.
5. **Answer:**
- Provide the probability to 4-decimal places or as a percentage rounded to 1-digit.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2743f58a-999a-485c-8435-d316e3b49890%2Fedc81a5a-29a6-4ea3-baab-7499506d2ccc%2Ftntyz2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 18:**
The weight of a full-term newborn baby follows a normal distribution with a mean weight of 7.5 pounds and a standard deviation of 1.8 pounds. Find the probability that the mean weight of a sample of 20 full-term newborn babies is less than 8.6 pounds. **SHOW WORK** and round your answer to 4-decimal places or answer as a percent with a 1-digit value.
---
**Solution Explanation:**
1. **Identify the Parameters:**
- Population mean (\(\mu\)) = 7.5 pounds
- Population standard deviation (\(\sigma\)) = 1.8 pounds
- Sample size (\(n\)) = 20
2. **Calculate the Standard Error (SE):**
\[
SE = \frac{\sigma}{\sqrt{n}} = \frac{1.8}{\sqrt{20}}
\]
3. **Find the Z-score:**
- We want the probability that the sample mean is less than 8.6 pounds.
- Compute the Z-score using:
\[
Z = \frac{\bar{X} - \mu}{SE} = \frac{8.6 - 7.5}{SE}
\]
4. **Use the Z-table:**
- Look up the computed Z-score in the standard normal distribution table to find the probability.
5. **Answer:**
- Provide the probability to 4-decimal places or as a percentage rounded to 1-digit.
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