13th Edition

ISBN: 9780134596839

Author: MCCLAVE

Publisher: PEARSON

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Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could co…

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a…

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Textbook Question

Chapter 4.6, Problem 4.94LM

Suppose x is a normally distributed random variable with µ = 50 and σ = 3. Find a value of the random variable, call it x₀, such that

a. P (x ≤ x₀) = .8413
b. P (x > x₀) = .025
c. P (x > x₀) = .95
d. P (41 ≤ x < x₀) = .8630
e. 10% of the values of x are less than x₀.
f. 1% of the values of x are greater than x₀.

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 4.6, Problem 4.93LM

Chapter 4.6, Problem 4.95LM

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Solution Summary: The author explains how the random variable X follows a normal distribution with mean mu =50 and standard deviation

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