Answered: Sarah has decided to plant white oak…

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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Question

Sarah has decided to plant white oak and soybeans. White oak acorns have a successful germination rate that follows a near-normal distribution of ?????????????? ~ ?(48, 2.4). Soybean seeds tend to have a higher successful germination rate, which follows a near-normal distribution of ?????????????????? ~ ?(89, 1.73). After a poor growing season, Sarah notices that only 43% of her white oak have germinated, and only 85% of her soybeans have germinated. Which plant has performed best?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1: Part 1

To determine which plant has performed better, we compared the actual germination rates for both white oak and soybeans with their respective expected germination rates.

1. White Oak:

- Expected germination rate: \(X \sim \mathcal{N}(48, 2.4)\)

- Actual germination rate: 43%

2. Soybeans:

- Expected germination rate: \(Y \sim \mathcal{N}(89, 1.73)\)

- Actual germination rate: 85%

Now, we need to compare the actual rates with the expected rates for both plants.