This exercise requires the use of a graphing calculator or computer programmed to do numerical integration. The normal distribution curve, which models the distributions of data in a wide range of app the function 1. P(x) = where = 3.14159265. and o and u are constants called the standard deviation and the mean, respectively. Its graph (for o = 1 and u = 2) is shown in the figure. 0.3 02 0.1 -1 I 2 3 45 With a = 3 and µ = 0, approximate p(x) dx. (Round your answer to four decimal places.)
This exercise requires the use of a graphing calculator or computer programmed to do numerical integration. The normal distribution curve, which models the distributions of data in a wide range of app the function 1. P(x) = where = 3.14159265. and o and u are constants called the standard deviation and the mean, respectively. Its graph (for o = 1 and u = 2) is shown in the figure. 0.3 02 0.1 -1 I 2 3 45 With a = 3 and µ = 0, approximate p(x) dx. (Round your answer to four decimal places.)
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![This exercise requires the use of a graphing calculator or computer programmed to do numerical integration. The normal distribution curve, which models the distributions of data in a wide range of applications, is given by the function
\[ p(x) = \frac{1}{\sqrt{2\pi} \sigma} e^{-\frac{(x - \mu)^2}{2\sigma^2}}, \]
where \(\pi = 3.14159265\ldots\) and \(\sigma\) and \(\mu\) are constants called the standard deviation and the mean, respectively. Its graph (for \(\sigma = 1\) and \(\mu = 2\)) is shown in the figure.
The graph is a bell-shaped curve, representing a normal distribution. It shows \(f(x)\) on the vertical axis and \(x\) on the horizontal axis. The peak of the curve is at \(x = 2\), indicating the mean. The curve is symmetric around the mean.
**With \(\sigma = 3\) and \(\mu = 0\), approximate \(\int_{0}^{+\infty} p(x) \, dx\). (Round your answer to four decimal places.)**
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Transcribed Image Text:This exercise requires the use of a graphing calculator or computer programmed to do numerical integration. The normal distribution curve, which models the distributions of data in a wide range of applications, is given by the function
\[ p(x) = \frac{1}{\sqrt{2\pi} \sigma} e^{-\frac{(x - \mu)^2}{2\sigma^2}}, \]
where \(\pi = 3.14159265\ldots\) and \(\sigma\) and \(\mu\) are constants called the standard deviation and the mean, respectively. Its graph (for \(\sigma = 1\) and \(\mu = 2\)) is shown in the figure.
The graph is a bell-shaped curve, representing a normal distribution. It shows \(f(x)\) on the vertical axis and \(x\) on the horizontal axis. The peak of the curve is at \(x = 2\), indicating the mean. The curve is symmetric around the mean.
**With \(\sigma = 3\) and \(\mu = 0\), approximate \(\int_{0}^{+\infty} p(x) \, dx\). (Round your answer to four decimal places.)**
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