If X~B(n=1000; P=.2) compute the following: SD(X) = 0x is : 8.21 9.45 12.65 16.46
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
![**Question: Calculating the Standard Deviation for a Binomial Distribution**
Given a binomial distribution \(X \sim B(n=1000, P=0.2)\), compute the standard deviation \(SD(X) = \sigma_X\):
### Options:
- \( \) 8.21
- \( \) 9.45
- \( \) 12.65
- \( \) 16.46
### Detailed Solution:
To find the standard deviation of a binomial distribution, use the formula:
\[ \sigma_X = \sqrt{n \cdot P \cdot (1 - P)} \]
Where:
- \(n\) is the number of trials.
- \(P\) is the probability of success on a single trial.
Given:
- \(n = 1000\)
- \(P = 0.2\)
- \(1 - P = 0.8\)
Substitute the values into the formula:
\[ \sigma_X = \sqrt{1000 \cdot 0.2 \cdot 0.8} \]
Now, calculate:
\[ \sigma_X = \sqrt{1000 \cdot 0.16} \]
\[ \sigma_X = \sqrt{160} \]
\[ \sigma_X \approx 12.65 \]
Thus, the correct answer is:
- \( \) 8.21
- \( \) 9.45
- \(x\) 12.65
- \( \) 16.46](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd529b6da-11b0-40e5-85fb-f211e59fb34e%2Fcd0b15ea-ec9a-49dd-9b38-929dbe87c973%2Fbvnzow6.png&w=3840&q=75)
Given Information
X ~ B(N=1000,p = 0.2)
Standard deviation is given by
So, Option C is correct i.e σx = 12.65
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