The IQ scores for adults roughly follow the normal...

The IQ scores for adults roughly follow the normal distribution $y=0.0266 e^{-(x-100)^{2 / 450}}$ $70 \leq x \leq 115,$ where $x$ is the IQ score.
(a) Use a graphing utility to graph the function.
(b) Use the graph in part (a) to estimate the average IQ score.

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Key Concepts

Normal Distribution

The normal distribution is a continuous probability distribution that is symmetric about its mean, forming a bell-shaped curve. It is defined by parameters such as the mean and standard deviation, which respectively determine the location of the peak and the spread of the curve. This distribution is widely used to model real-world phenomena where values cluster around an average with predictable deviations.

Mean

The mean is a measure of central tendency that represents the average value of a data set. In the context of a normal distribution, the mean is the point around which the curve is centered, and it corresponds to the highest point of the bell curve. It plays a crucial role in determining the symmetry and location of the data distribution.

Graphing Functions

Graphing functions, particularly probability density functions like those of the normal distribution, is a valuable technique in visualizing the behavior of data. By plotting these functions using graphing utilities, one can easily identify key features such as the peak (mean) and the spread of the distribution, which aids in understanding and interpreting statistical data.

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