Consider the following Binomial Experiment:  290 people have been exposed to the flu.  If the probability that a person contracting the flu on exposure is 0.49, find the variance of these 290 people contracting the flu.




 72.4710




 0.2499




 301.8367




 147.9000




 69.6290




 None of the above.

To find the variance in a binomial experiment, we use the formula:

\[ \text{Variance} = n \cdot p \cdot (1 - p) \]

where:
- \( n \) is the number of trials (in this case, the number of people exposed to the flu),
- \( p \) is the probability of success (in this case, the probability of contracting the flu on exposure).

Given:
- \( n = 290 \)
- \( p = 0.49 \)

Let's plug these values into the formula:

\[ \text{Variance} = 290 \cdot 0.49 \cdot (1 - 0.49) \]

First, calculate \( 1 - 0.49 \):

\[ 1 - 0.49 = 0.51 \]

Then, multiply all the terms together:

\[ \text{Variance} = 290 \cdot 0.49 \cdot 0.51 \]

Performing the multiplication:

\[ \text{Variance} = 290 \cdot 0.2499 \]
\[ \text{Variance} = 72.471 \]

Therefore, the variance of these 290 people contracting the flu is:

\[ \boxed{72.4710} \]

If you want further details or have any questions, please let me know!

Here are some related questions:
1. What is the definition of a binomial experiment?
2. How do you calculate the mean in a binomial distribution?
3. What are the key properties of a binomial distribution?
4. How is the standard deviation related to variance in a binomial distribution?
5. What is the significance of the probability \( p \) in a binomial distribution?
6. How can you interpret the variance in the context of real-world scenarios?
7. What assumptions must be met for a distribution to be considered binomial?
8. How does sample size \( n \) affect the variance in a binomial distribution?

**Tip:** Always ensure the probability value \( p \) is between 0 and 1 before using it in the variance formula.

Learn how to calculate the variance in a binomial experiment with a detailed example. Given 290 people exposed to the flu and a probability of 0.49, find the variance using the binomial distribution formula. Suitable for advanced high school and college students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation