Statistics for Business and Economics (13th Edition)

13th Edition

ISBN: 9780134506593

Author: James T. McClave, P. George Benson, Terry Sincich

Publisher: PEARSON

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Chapter 4.6, Problem 4.108ACI

Safety of underground tunnels. Research published in the journal Tunnelling and Underground Space Technology (July 2014) evaluated the safety of underground tunnels built in rigid soils. A factor of safety (FS), measured as the ratio of capacity over demand, was determined for three different areas of tunnels made from shotcrete: tunnel face, tunnel walls, and tunnel crown. FS was determined to be normally distributed in each area, with means and standard deviations shown in the table. Tunnel failure is considered to occur when FS is lower than or equal to 1. Which tunnel area is more likely to result in failure? Why?

	Mean (µ)	Standard Deviation (σ)
Tunnel Face	1.2	.16
Tunnel Walls	1.4	.20
Tunnel Crown	2.1	.70

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 4.107ACI

Chapter 4.6, Problem 4.109ACI

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Chapter 4 Solutions

Statistics for Business and Economics (13th Edition)

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Solution Summary: The author explains how to study the "Safety of Underground tunnels" Ratio of capacity over demand was determined for three different areas.

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