I would like to know the answer to 5b
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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I would like to know the answer to 5b
![### Educational Material on Statistics and Probability
---
#### Problem 4:
**4a) Normal Approximation:**
To solve Problem 4b using normal approximation:
\[
\mu = E(X) = np = 20 \times 0.065
\]
\[
\sigma = \sqrt{np(1-p)} = \sqrt{20 \times 0.065 \times (1-0.065)}
\]
Use the Z-table to find the probability \(P(X \leq 5)\).
---
#### Problem 5:
A patient is asked by her doctor to record her blood pressure at home. Over 10 days, she takes the readings detailed in the table below. The doctor wants to assess whether the true mean blood pressure is 125.
**Table of Blood Pressure Readings:**
| Days | Blood Pressure |
|------|----------------|
| 1 | 111 |
| 2 | 109 |
| 3 | 112 |
| 4 | 114 |
| 5 | 120 |
| 6 | 125 |
| 7 | 126 |
| 8 | 118 |
| 9 | 124 |
| 10 | 127 |
**5a) Provide a 95% Confidence Interval:**
To calculate the 95% confidence interval for the true mean blood pressure (\(t_{0.05/2} = 2.26\)):
\[
\bar{x} = 120.8
\]
\[
s = 8.2
\]
\[
\frac{s}{\sqrt{n}} = \frac{8.2}{\sqrt{10}} = 2.8
\]
\[
\text{Confidence Interval} = (110.2, 151.4)
\]
**5b) Answer the doctor's question based on the 95% CI:**
The confidence interval includes the mean blood pressure of 125, suggesting it is a plausible value for the true mean.
---
#### Problem 6:
A random sample of 67 lab rats is used to find the mean time it takes to run through a maze. A 95% confidence interval is constructed. Determine which of the statements are true:
**Statements:**
- More than 10% of the sample rats are expected to run the maze between](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4189f03-9019-46b8-8e5e-0667b7a39017%2F2910486f-fed1-4791-b831-bab535f6641c%2Fo5m6czw.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Material on Statistics and Probability
---
#### Problem 4:
**4a) Normal Approximation:**
To solve Problem 4b using normal approximation:
\[
\mu = E(X) = np = 20 \times 0.065
\]
\[
\sigma = \sqrt{np(1-p)} = \sqrt{20 \times 0.065 \times (1-0.065)}
\]
Use the Z-table to find the probability \(P(X \leq 5)\).
---
#### Problem 5:
A patient is asked by her doctor to record her blood pressure at home. Over 10 days, she takes the readings detailed in the table below. The doctor wants to assess whether the true mean blood pressure is 125.
**Table of Blood Pressure Readings:**
| Days | Blood Pressure |
|------|----------------|
| 1 | 111 |
| 2 | 109 |
| 3 | 112 |
| 4 | 114 |
| 5 | 120 |
| 6 | 125 |
| 7 | 126 |
| 8 | 118 |
| 9 | 124 |
| 10 | 127 |
**5a) Provide a 95% Confidence Interval:**
To calculate the 95% confidence interval for the true mean blood pressure (\(t_{0.05/2} = 2.26\)):
\[
\bar{x} = 120.8
\]
\[
s = 8.2
\]
\[
\frac{s}{\sqrt{n}} = \frac{8.2}{\sqrt{10}} = 2.8
\]
\[
\text{Confidence Interval} = (110.2, 151.4)
\]
**5b) Answer the doctor's question based on the 95% CI:**
The confidence interval includes the mean blood pressure of 125, suggesting it is a plausible value for the true mean.
---
#### Problem 6:
A random sample of 67 lab rats is used to find the mean time it takes to run through a maze. A 95% confidence interval is constructed. Determine which of the statements are true:
**Statements:**
- More than 10% of the sample rats are expected to run the maze between
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