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**Binomial Distribution Problem** A random variable is binomially distributed with parameters \(n = 16\) and \(\pi = 0.40\). The task is to determine the expected value and standard deviation of the variable. **Multiple Choice Options:** - A) 2.00 and 1.24 - B) 4.80 and 4.00 - C) 6.40 and 1.96 - D) 2.00 and 1.20 **Explanation:** To solve this, we need to understand the formulae for the expected value and standard deviation of a binomial distribution: **Expected Value (Mean):** \[ E(X) = n \times \pi \] **Standard Deviation:** \[ \sigma = \sqrt{n \times \pi \times (1 - \pi)} \] Using the given values: - \(n = 16\) - \(\pi = 0.40\) We can calculate as follows: - \(E(X) = 16 \times 0.40 = 6.40\) - \(\sigma = \sqrt{16 \times 0.40 \times 0.60} = \sqrt{3.84} \approx 1.96\) Thus, the correct answer is C) 6.40 and 1.96.

**Binomial Distribution Problem** A random variable is binomially distributed with parameters \(n = 16\) and \(\pi = 0.40\). The task is to determine the expected value and standard deviation of the variable. **Multiple Choice Options:** - A) 2.00 and 1.24 - B) 4.80 and 4.00 - C) 6.40 and 1.96 - D) 2.00 and 1.20 **Explanation:** To solve this, we need to understand the formulae for the expected value and standard deviation of a binomial distribution: **Expected Value (Mean):** \[ E(X) = n \times \pi \] **Standard Deviation:** \[ \sigma = \sqrt{n \times \pi \times (1 - \pi)} \] Using the given values: - \(n = 16\) - \(\pi = 0.40\) We can calculate as follows: - \(E(X) = 16 \times 0.40 = 6.40\) - \(\sigma = \sqrt{16 \times 0.40 \times 0.60} = \sqrt{3.84} \approx 1.96\) Thus, the correct answer is C) 6.40 and 1.96.

MATLAB: An Introduction with Applications
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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**Binomial Distribution Problem** A random variable is binomially distributed with parameters \(n = 16\) and \(\pi = 0.40\). The task is to determine the expected value and standard deviation of the variable. **Multiple Choice Options:** - A) 2.00 and 1.24 - B) 4.80 and 4.00 - C) 6.40 and 1.96 - D) 2.00 and 1.20 **Explanation:** To solve this, we need to understand the formulae for the expected value and standard deviation of a binomial distribution: **Expected Value (Mean):** \[ E(X) = n \times \pi \] **Standard Deviation:** \[ \sigma = \sqrt{n \times \pi \times (1 - \pi)} \] Using the given values: - \(n = 16\) - \(\pi = 0.40\) We can calculate as follows: - \(E(X) = 16 \times 0.40 = 6.40\) - \(\sigma = \sqrt{16 \times 0.40 \times 0.60} = \sqrt{3.84} \approx 1.96\) Thus, the correct answer is C) 6.40 and 1.96.
Transcribed Image Text:**Binomial Distribution Problem** A random variable is binomially distributed with parameters \(n = 16\) and \(\pi = 0.40\). The task is to determine the expected value and standard deviation of the variable. **Multiple Choice Options:** - A) 2.00 and 1.24 - B) 4.80 and 4.00 - C) 6.40 and 1.96 - D) 2.00 and 1.20 **Explanation:** To solve this, we need to understand the formulae for the expected value and standard deviation of a binomial distribution: **Expected Value (Mean):** \[ E(X) = n \times \pi \] **Standard Deviation:** \[ \sigma = \sqrt{n \times \pi \times (1 - \pi)} \] Using the given values: - \(n = 16\) - \(\pi = 0.40\) We can calculate as follows: - \(E(X) = 16 \times 0.40 = 6.40\) - \(\sigma = \sqrt{16 \times 0.40 \times 0.60} = \sqrt{3.84} \approx 1.96\) Thus, the correct answer is C) 6.40 and 1.96.
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