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Chapter 28: Problem 3

What is a normal distribution? Discuss this curve with regard to quantitative traits within a population. What is the relationship between the standard deviation and the normal distribution?

Short Answer

Expert verified
A normal distribution is a bell-shaped curve that is symmetric about its mean, and is widely observed in phenomena having a large number of small effects, such as quantitative traits within a population. The standard deviation, a measure of variability, controls the spread of the normal distribution: a smaller standard deviation results in a narrower curve while a larger one results in a wider curve.

Step by step solution

01

Define Normal Distribution

A normal distribution, also known as a Gaussian distribution, is a type of continuous probability distribution for a real-valued random variable. It is a bell-shaped curve symmetric about its mean. Its peak represents the highest probability of occurrence, and it tapers away on either side.
02

Discuss the Normal Distribution in Relation to Quantitative Traits

When it comes to quantitative traits within a population, a normal distribution often occurs. It suggests that traits are controlled by a large number of genes, each with a small effect. The distribution of these traits in population often forms a bell-shaped curve where most individuals have an average value for the trait and only few individuals have extreme values.
03

Explain the Relationship Between the Standard Deviation and Normal Distribution

Standard deviation is a measure of the amount of variation or dispersion of a set of values. In a normal distribution, about 68% of the data falls within one standard deviation of the mean. 95% falls within two standard deviations and 99.7% fall within three standard deviations. This means that if the standard deviation is small, the data points are close to the mean, thus the bell-shaped curve will be narrow. Conversely, a large standard deviation means that the data points are spread out over a wider range of values, thus the bell-shaped curve will be wider. Therefore, the standard deviation controls the spread of the normal distribution.

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