(A) Explanation Formula used: The probability of a continuous random variable X with its density function f ( x ) = 1 σ 2 π e − ( x − μ 2 σ ) 2 on the interval [ c , d ] : P ( c ≤ X ≤ d ) = 1 σ 2 π ∫ c d e − ( x − μ ) 2 ( 2 σ 2 ) d x , where μ is mean as well as median and σ > 0 is standard deviation. Calculation: Compute the probability range for the random variable X with μ = 0 and σ = 0.5 . Substitute μ = 0 and σ = 0.5 in P ( μ − 2 σ ≤ X ≤ μ + 2 σ ) and simplify. P ( μ − 2 σ ≤ X ≤ μ + 2 σ ) = P ( 0 − 2 ( 0.5 ) ≤ X ≤ 0 + 2 ( 0.5 ) ) = P ( 0 − 1 ≤ X ≤ 0 + 1 ) = P ( − 1 ≤ X ≤ 1 ) By the above formula, the value of P ( − 1 ≤ X ≤ 1 ) = 1 ( 0 (B) To determine To approximate: The probability P ( μ − 2 σ ≤ X ≤ μ + 2 σ ) to four decimal places with μ = 0 and σ = 1 . (C) To determine To approximate: The probability P ( μ − 2 σ ≤ X ≤ μ + 2 σ ) to four decimal places with μ = 0 and σ = 2 using graphing calculator.

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

15th Edition

ISBN: 9781323047620

Author: Barnett, Ziegler, Byleen

Publisher: Pearson Education

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Chapter 11.4, Problem 56E

(A)

To determine

To approximate: The probability P(μ−2σ≤X≤μ+2σ) to four decimal places with μ=0 and σ=0.5.

(B)

To determine

To approximate: The probability P(μ−2σ≤X≤μ+2σ) to four decimal places with μ=0 and σ=1.

(C)

To determine

To approximate: The probability P(μ−2σ≤X≤μ+2σ) to four decimal places with μ=0 and σ=2 using graphing calculator.

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Chapter 11.4, Problem 55E

Chapter 11.4, Problem 57E

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Chapter 11 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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To approximate: The probability P ( μ − 2 σ ≤ X ≤ μ + 2 σ ) to four decimal places with μ = 0 and σ = 0.5 .

Solution Summary: The author calculates the probability of a continuous random variable X with its density function f(x)=1sigma

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To approximate: The probability P(μ−2σ≤X≤μ+2σ) to four decimal places with μ=0 and σ=0.5.

To approximate: The probability P(μ−2σ≤X≤μ+2σ) to four decimal places with μ=0 and σ=1.

To approximate: The probability P(μ−2σ≤X≤μ+2σ) to four decimal places with μ=0 and σ=2 using graphing calculator.

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Chapter 11 Solutions