Find the mean, variance, and standard deviation of the binomial distribution with the given values of and .

The mean, , is 56.0 . (Round to the nearest tenth as needed.)
The variance, , is . (Round to the nearest tenth as needed.)

Ask by Martin Lindsey. in the United States

Jan 21,2025

Question

Find the mean, variance, and standard deviation of the binomial distribution with the given values of and .

The mean, , is 56.0 . (Round to the nearest tenth as needed.)
The variance, , is . (Round to the nearest tenth as needed.)

Ask by Martin Lindsey. in the United States

Jan 21,2025

UpStudy AI · Accepted Answer

To determine the **mean ($$ \mu $$)**, **variance ($$ \sigma^{2} $$)**, and **standard deviation ($$ \sigma $$)** of a binomial distribution with parameters $$ n = 80 $$ and $$ p = 0.7 $$, we use the following formulas:

1. **Mean ($$ \mu $$)**:
   $$
   \mu = n \times p = 80 \times 0.7 = 56.0
   $$
   
2. **Variance ($$ \sigma^{2} $$)**:
   $$
   \sigma^{2} = n \times p \times (1 - p) = 80 \times 0.7 \times 0.3 = 16.8
   $$
   
3. **Standard Deviation ($$ \sigma $$)**:
   $$
   \sigma = \sqrt{\sigma^{2}} = \sqrt{16.8} \approx 4.1
   $$
   
**Final Results**:
- **Mean ($$ \mu $$)**: 56.0
- **Variance ($$ \sigma^{2} $$)**: **16.8**
- **Standard Deviation ($$ \sigma $$)**: 4.1
The variance ($$ \sigma^{2} $$) is 16.8.

Find the mean, variance, and standard deviation of the binomial distribution with the given values of and .

The mean, , is 56.0 . (Round to the nearest tenth as needed.)
The variance, , is . (Round to the nearest tenth as needed.)

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Statistics Questions

Find the mean, variance, and standard deviation of the binomial distribution with the given values of and . The mean, , is 56.0 . (Round to the nearest tenth as needed.) The variance, , is . (Round to the nearest tenth as needed.)

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Statistics Questions

Find the mean, variance, and standard deviation of the binomial distribution with the given values of and .

The mean, , is 56.0 . (Round to the nearest tenth as needed.)
The variance, , is . (Round to the nearest tenth as needed.)