Explanation Formula used: “The number of standard deviations a measurement x is from a mean μ is given by z = x − μ σ where μ is the mean, σ is the standard deviation and x − μ is the distance between x and μ ”. Calculation: Given that the mean is − 10 , the standard deviation is 5 and the given interval is [ − 3 , ∞ ) . The standard form of the probability density function of this normal distribution is f ( x ) = 1 σ 2 π e − ( x − μ ) 2 2 σ 2 , where μ is the mean and σ is the standard deviation. Substitute μ = − 10 and σ = 5 in f ( x ) = 1 σ 2 π e − ( x − μ ) 2 2 σ 2 as, f ( x ) = 1 σ 2 π e − ( x − μ ) 2 2 σ 2 = 1 ( 5 ) 2 π e − ( x − ( − 10 ) ) 2 2 ( 5 ) 2 = 1 5 2 π e − ( x + 10 ) 2 50 Thus, the probability density function of this normal distribution becomes f ( x ) = 1 5 2 π e − ( x + 10 ) 2 50

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Author: Barnett

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Chapter 11.4, Problem 32E

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To find: The area under the normal curve and above the interval [−3,∞).

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Chapter 11.4, Problem 31E

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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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The area under the normal curve and above the interval [ − 3 , ∞ ) .

Solution Summary: The author calculates that the area under the normal curve and above the interval is 0.0808.

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To find: The area under the normal curve and above the interval [−3,∞).

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Chapter 11 Solutions