Explanation Given: The maximum daily temperature is uniform which ranges from 27 ° C to 42 ° C . Definition used: 1. Uniform Distribution : If X is a random variable with probability density function f ( x ) = 1 b − a for x in [ a , b ] . Then, μ = 1 2 ( b + a ) and σ = 1 12 ( b − a ) . 2. Probability density function on ( − ∞ , ∞ ) : If f is a probability density function for a random variable X in the interval ( − ∞ , ∞ ) , then 1. P ( X ≤ b ) = P ( X < b ) = ∫ − ∞ b f ( x ) d x 2. P ( X ≥ a ) = P ( X > a ) = ∫ a ∞ f ( x ) d x 3. P ( − ∞ < X < ∞ ) = ∫ − ∞ ∞ f ( x ) d x = 1 . Calculation: Given that, the maximum daily temperature is uniform ranges from 27 ° C to 42 ° C . Thus, the difference of the temperature is, 42 ° C − 27 ° C = 15 ° C . The uniform distribution for the maximum daily temperature T is f ( t ) = 1 15 on the interval [ 27 , 42 ]

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 18.3, Problem 1YT

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To find: The expected maximum temperature and the probability that the maximum temperature will be within one standard deviation of the mean.

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Chapter 18.2, Problem 43E

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Chapter 18 Solutions

Finite Mathematics and Calculus with Applications (10th Edition)

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The expected maximum temperature and the probability that the maximum temperature will be within one standard deviation of the mean.

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Chapter 18 Solutions