Consider a normal distribution with first quartileQ1=74.95points and third quartileQ3=83.05points. (a) Find the meanμof the distribution.(b) Find the standard deviationσof the distribution.

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Answered: (a) Find the mean μ of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider a normal distribution with first quartile

Q1=74.95

points and third quartile

Q3=83.05

points.

(a) Find the mean

of the distribution.

(b) Find the standard deviation

of the distribution.

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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