Explain the Role of Area in the Normal Density Function $\mu = 2200$

question 91

Short Answer

Explain the Role of Area in the Normal Density Function
-The weight of 2-year old hyraxes is known to be normally distributed with mean $\mu = 2200$ grams and standard deviation $\sigma = 365$ grams
(a) Draw a normal curve with the parameters labeled.
(b) Shade the region that represents the proportion of hyraxes who weighed more than 2930 grams.
(c) Suppose the area under the normal curve to the left of $X = 2930$ is $0.0228$ . Provide two interpretations of this result.

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Definitions:

Normal Distributions

A symmetrical, bell-shaped distribution of data in which most of the data points cluster around a central peak and the probabilities for values further away from the mean taper off equally in both directions.

Mathematical Formulas

A concise way of expressing information symbolically, as in a mathematical or chemical formula.

Frequency Distributions

A way to organize data that shows how often each value occurs.

Normal Distributions

A probability distribution that is symmetric about its mean, showing that near the mean there's a higher likelihood of occurrence, a foundational concept in statistics.