Assume that a procedure yields a binomial distribution with n=1348 trials and the probability of succe for one trial is p 52%. Find the mean for this binomial distribution. (Round answer to one decimal place.) f Find the standard deviation for this distribution. (Round answer to two decimal places.) Use the range rule of thumb to find the minimum usual value u-20 and the maximum usual value µ+20. Enter answer as an interval using square-brackets only with whole numbers.
Assume that a procedure yields a binomial distribution with n=1348 trials and the probability of succe for one trial is p 52%. Find the mean for this binomial distribution. (Round answer to one decimal place.) f Find the standard deviation for this distribution. (Round answer to two decimal places.) Use the range rule of thumb to find the minimum usual value u-20 and the maximum usual value µ+20. Enter answer as an interval using square-brackets only with whole numbers.
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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![**Understanding Binomial Distribution**
---
### Problem Statement:
Assume that a procedure yields a binomial distribution with \( n = 1348 \) trials and the probability of success for one trial is \( p = 52\% \).
1. **Find the mean for this binomial distribution.**
*(Round answer to one decimal place.)*
\[
\mu = \_\_\_
\]
2. **Find the standard deviation for this distribution.**
*(Round answer to two decimal places.)*
\[
\sigma = \_\_\_
\]
3. **Use the range rule of thumb to find the minimum usual value \(\mu - 2\sigma\) and the maximum usual value \(\mu + 2\sigma\).**
Enter answer as an interval using square-brackets only with whole numbers.
\[
\text{usual values} = \_\_\_
\]
### Solution Outline:
- **Calculation of Mean (\(\mu\)):**
For a binomial distribution, the mean (\(\mu\)) is given by:
\[
\mu = n \cdot p
\]
where:
\[
n = 1348 \quad \text{and} \quad p = 0.52
\]
- **Calculation of Standard Deviation (\(\sigma\)):**
For a binomial distribution, the standard deviation (\(\sigma\)) is given by:
\[
\sigma = \sqrt{n \cdot p \cdot (1 - p)}
\]
- **Use of Range Rule of Thumb:**
To find the usual range, calculate:
\[
\mu - 2\sigma \quad \text{and} \quad \mu + 2\sigma
\]
### Step-by-Step Solution:
1. **Mean Calculation:**
\[
\mu = n \cdot p = 1348 \cdot 0.52
\]
\(\mu = \_\_\_ \) (rounding to one decimal place)
2. **Standard Deviation Calculation:**
\[
\sigma = \sqrt{1348 \cdot 0.52 \cdot 0.48}
\]
\(\sigma = \_\_\_\) (rounding to two](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc260e632-e4e2-45c7-853f-2d07e95220d0%2F811fccaa-3ef7-4d97-a252-70cff1aa253a%2Feb64dqp_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Binomial Distribution**
---
### Problem Statement:
Assume that a procedure yields a binomial distribution with \( n = 1348 \) trials and the probability of success for one trial is \( p = 52\% \).
1. **Find the mean for this binomial distribution.**
*(Round answer to one decimal place.)*
\[
\mu = \_\_\_
\]
2. **Find the standard deviation for this distribution.**
*(Round answer to two decimal places.)*
\[
\sigma = \_\_\_
\]
3. **Use the range rule of thumb to find the minimum usual value \(\mu - 2\sigma\) and the maximum usual value \(\mu + 2\sigma\).**
Enter answer as an interval using square-brackets only with whole numbers.
\[
\text{usual values} = \_\_\_
\]
### Solution Outline:
- **Calculation of Mean (\(\mu\)):**
For a binomial distribution, the mean (\(\mu\)) is given by:
\[
\mu = n \cdot p
\]
where:
\[
n = 1348 \quad \text{and} \quad p = 0.52
\]
- **Calculation of Standard Deviation (\(\sigma\)):**
For a binomial distribution, the standard deviation (\(\sigma\)) is given by:
\[
\sigma = \sqrt{n \cdot p \cdot (1 - p)}
\]
- **Use of Range Rule of Thumb:**
To find the usual range, calculate:
\[
\mu - 2\sigma \quad \text{and} \quad \mu + 2\sigma
\]
### Step-by-Step Solution:
1. **Mean Calculation:**
\[
\mu = n \cdot p = 1348 \cdot 0.52
\]
\(\mu = \_\_\_ \) (rounding to one decimal place)
2. **Standard Deviation Calculation:**
\[
\sigma = \sqrt{1348 \cdot 0.52 \cdot 0.48}
\]
\(\sigma = \_\_\_\) (rounding to two
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