17th Edition

ISBN: 9781938168062

Author: Gilbert Strang, Edwin Jed Herman

Publisher: OpenStax

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Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

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Textbook Question

Chapter 6.4, Problem 237E

[T] Suppose that a set of standardized test scores is normally distributed with mean μ = 100 and standard deviation σ = 10. Set up an integral that represents the probability that a test score will be between 90 and 110 and use the integral of the degree 10 Maclaurin polynomial of 1 2 π e − x 2 / 2 to estimate this probability.

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.

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Chapter 6.4, Problem 236E

Chapter 6.4, Problem 238E

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