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 [ − 18 , − 12 ] . To find the area above [ − 18 , − 12 ] subtract the area above [ − 12 , − 10 ] from the area above [ − 18 , − 10 ] . First obtain the area above [ − 18 , − 10 ] . Therefore, substitute μ = − 10 , σ = 5 , and x = − 18 in the above equation. z = − 18 − ( − 10 ) 5 = − 8 5 = − 1.6 Since the normal curves are symmetrical with respect to a vertical line through the mean, the area corresponding to z = − 1.6 is same as the area corresponding to z = 1

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ISBN: 9780137554805

Author: Raymond Barnett, Michael Ziegler

Publisher: PEARSON+

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Chapter 11.4, Problem 30E

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To find: The area under the normal curve and above the interval [−18,−12].

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Chapter 11.4, Problem 29E

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Chapter 11 Solutions

Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

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 [ − 18 , − 12 ] .

Solution Summary: The author calculates the area under the normal curve and above the interval left[18,-12right].

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To find: The area under the normal curve and above the interval [−18,−12].

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Chapter 11 Solutions