Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.25 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 36. Complete parts (a) through (c) below. a. Find the mean and the standard deviation for the numbers of peas with green pods in the groups of 36. The value of the mean is μ = peas. (Type an integer or a decimal. Do not round.)
Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.25 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 36. Complete parts (a) through (c) below. a. Find the mean and the standard deviation for the numbers of peas with green pods in the groups of 36. The value of the mean is μ = peas. (Type an integer or a decimal. Do not round.)
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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![**Pea Hybridization Experiment**
Consider an experiment where peas are hybridized, and there is a 0.25 probability for a pea to have green pods. In this scenario, offspring peas are randomly grouped in sets of 36. Let's analyze the data and answer the following questions:
---
**Part (a): Calculating the Mean and Standard Deviation**
1. **Mean (\( \mu \)) Calculation**: Determine the average number of peas with green pods in a group of 36.
- **Formula**: \( \mu = n \times p \)
- \( n \) = number of trials (peas in a group) = 36
- \( p \) = probability of success (pea having green pods) = 0.25
- **Calculation**:
- \( \mu = 36 \times 0.25 = \) [Insert your answer here]
2. **Standard Deviation (\( \sigma \)) Calculation**: Determine the variability of the number of peas with green pods.
- **Formula**: \( \sigma = \sqrt{n \times p \times (1-p)} \)
- \( (1-p) \) = probability of failure (pea not having green pods)
- **Calculation**:
- \( \sigma = \sqrt{36 \times 0.25 \times 0.75} = \) [Calculate and insert answer here]
Ensure your answers for mean and standard deviation are either integers or decimals and do not round them.
---
This educational exercise aims to familiarize students with basic statistical calculations in probability experiments, illustrating mean and standard deviation concepts in practical applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c582252-6541-4096-9706-b4f3b52fcf1c%2Fc2a0cb0e-380c-4e4d-9a28-9a7549f452be%2Fauy6e2a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Pea Hybridization Experiment**
Consider an experiment where peas are hybridized, and there is a 0.25 probability for a pea to have green pods. In this scenario, offspring peas are randomly grouped in sets of 36. Let's analyze the data and answer the following questions:
---
**Part (a): Calculating the Mean and Standard Deviation**
1. **Mean (\( \mu \)) Calculation**: Determine the average number of peas with green pods in a group of 36.
- **Formula**: \( \mu = n \times p \)
- \( n \) = number of trials (peas in a group) = 36
- \( p \) = probability of success (pea having green pods) = 0.25
- **Calculation**:
- \( \mu = 36 \times 0.25 = \) [Insert your answer here]
2. **Standard Deviation (\( \sigma \)) Calculation**: Determine the variability of the number of peas with green pods.
- **Formula**: \( \sigma = \sqrt{n \times p \times (1-p)} \)
- \( (1-p) \) = probability of failure (pea not having green pods)
- **Calculation**:
- \( \sigma = \sqrt{36 \times 0.25 \times 0.75} = \) [Calculate and insert answer here]
Ensure your answers for mean and standard deviation are either integers or decimals and do not round them.
---
This educational exercise aims to familiarize students with basic statistical calculations in probability experiments, illustrating mean and standard deviation concepts in practical applications.
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