STATISTICS FOR ENGR.+SCI.(LL)-W/ACCESS
4th Edition
ISBN: 9781260133295
Author: Navidi
Publisher: MCG
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Textbook Question
Chapter 3.4, Problem 18E
The vertical displacement v of a cracked slurry infiltrated fiber concrete member at maximum shear stress is given by v = a + bw, where w is the crack width, and a and b are estimated from data to be a = 2.5 ± 0.1 mm and b = 0.05 ± 0.01. Assume that w = 1.2 ± 0.1 mm.
- a. Estimate v, and find the uncertainty in the estimate.
- b. Of the uncertainties in w, a, and b, only one has a non-negligible effect on the uncertainty in v. Which one is it?
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The vertical displacement v of a cracked slurry infiltrated fiber concrete member at maximum shear stress is given by v = a + bw, where w is the crack width, and a and b are estimated from data to be a = 2.5 ± 0.1 mm and b = 0.05 ± 0.01. Assume that w = 1.2 ± 0.1 mm.a) Estimate v, and find the uncertainty in the estimate.b) Of the uncertainties in w, a, and b, only one has a non-negligible effect on the uncertainty in v. Which one is it?
In the article “Influence of Crack Width on Shear Behaviour of SIFCON” (C. Fritz and H. Reinhardt, High Performance Fiber Reinforced Cement Composites: Proceedings of the International RILEM/ACI Workshop, 1992), the maximum shear stress τ of a cracked concrete member is given to be τ = τ0(1 − kw), where τ0 is the maximum shear stress for a crack width of zero, w is the crack width in mm, and k is a constant estimated from experimental data. Assume k = 0.29 ± 0.05 mm−1. Given that τ0 = 50 MPa and w = 1.0 mm, both with negligible uncertainty, estimate τ and find the uncertainty in the estimate.
As an industrial engineer is working a test of material used to on a certain product to determine whether it is more economical to repair a damaged area rather than replace the entire structure. The engineer obtained the following data on the bond length (x variable) vs. the rupture load (y variable)
Bond Length (mm)
Rupture Load (N)
50
17,052
50
14,063
80
26,264
80
19,600
110
21,952
110
26,362
140
26,362
140
26,754
170
31,654
170
32,928
Find the 95% Confidence Interval for the conditional mean of the response variable at x = 140
Chapter 3 Solutions
STATISTICS FOR ENGR.+SCI.(LL)-W/ACCESS
Ch. 3.1 - The boiling point of water is measured four times....Ch. 3.1 - Two thermometers are calibrated by measuring the...Ch. 3.1 - The weight of an object is given as 67.2 0.3 g....Ch. 3.1 - Prob. 4ECh. 3.1 - A person stands on a bathroom scale. The reading...Ch. 3.1 - A person gets on and off a bathroom scale four...Ch. 3.1 - In a hypothetical scenario, the National Institute...Ch. 3.1 - Prob. 8ECh. 3.1 - A new and unknown weight is weighed on the same...Ch. 3.1 - Prob. 10E
Ch. 3.1 - The length of a rod was measured eight times. The...Ch. 3.2 - Assume that X and Y are independent measurements...Ch. 3.2 - The length of a rod is to be measured by a process...Ch. 3.2 - The volume of a cone is given by V = r2h/3, where...Ch. 3.2 - In the article The Worlds Longest Continued Series...Ch. 3.2 - A cylindrical hole is bored through a steel block,...Ch. 3.2 - A force of F = 2.2 0.1 N is applied to a block...Ch. 3.2 - The period T of a simple pendulum is given by...Ch. 3.2 - The specific gravity of a substance is given by G...Ch. 3.2 - Prob. 10ECh. 3.2 - According to Newtons law of cooling, the...Ch. 3.2 - Prob. 12ECh. 3.2 - Nine independent measurements are made of the...Ch. 3.2 - A certain scale has an uncertainty of 3 g and a...Ch. 3.2 - The volume of a rock is measured by placing the...Ch. 3.2 - A student measures the spring constant k of a...Ch. 3.2 - A certain chemical process is run 10 times at a...Ch. 3.2 - An object is weighed four times, and the results,...Ch. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.3 - Find the uncertainty in Y, given that X = 2.0 0.3...Ch. 3.3 - Given that X and Y are related by the given...Ch. 3.3 - The volume of a cone is given by V = r2h/3, where...Ch. 3.3 - Prob. 4ECh. 3.3 - The period T of a simple pendulum is given by...Ch. 3.3 - The change in temperature of an iron bar brought...Ch. 3.3 - The friction velocity F of water flowing through a...Ch. 3.3 - The refractive index n of a piece of glass is...Ch. 3.3 - The density of a rock will be measured by placing...Ch. 3.3 - The conversion of ammonium cyanide to urea is a...Ch. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - The acceleration g due to gravity is estimated by...Ch. 3.3 - Refer to Exercise 4. Assume that T = 298.4 0.2 K....Ch. 3.3 - Refer to Exercise 5. a. Assume g = 9.80 m/s2...Ch. 3.3 - Refer to Exercise 6. Assume that c = 448 J/kgC and...Ch. 3.3 - Prob. 17ECh. 3.3 - Refer to Exercise 8. Assume the critical angle is...Ch. 3.3 - Refer to Exercise 9. Assume that the mass of the...Ch. 3.3 - Prob. 20ECh. 3.4 - Find the uncertainty in U, assuming that X = 10.0 ...Ch. 3.4 - The volume of a cone is given by V = r2h/3, where...Ch. 3.4 - From a fixed point on the ground, the distance to...Ch. 3.4 - Refer to Exercise 10 in Section 3.2. Assume that ...Ch. 3.4 - When air enters a compressor at pressure P1 and...Ch. 3.4 - One way to measure the water content of a soil is...Ch. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - The Beer-Lambert law relates the absorbance A of a...Ch. 3.4 - In the article Temperature-Dependent Optical...Ch. 3.4 - Refer to Exercise 12 in Section 3.2. Assume that 0...Ch. 3.4 - Prob. 12ECh. 3.4 - Archaeologists studying meat storage methods...Ch. 3.4 - Prob. 14ECh. 3.4 - A cylindrical wire of radius R elongates when...Ch. 3.4 - Prob. 16ECh. 3.4 - Refer to Exercise 16. In an experiment to...Ch. 3.4 - The vertical displacement v of a cracked slurry...Ch. 3.4 - The shape of a bacterium can be approximated by a...Ch. 3.4 - Prob. 20ECh. 3.4 - Refer to Exercise 10 in Section 3.2. Assume that ...Ch. 3.4 - Refer to Exercise 5. Assume that P1 = 15.3 0.2...Ch. 3.4 - Refer to Exercise 7. Assume that p = 4.3 0.1 cm...Ch. 3.4 - Prob. 24ECh. 3.4 - Refer to Exercise 12. Estimate n, and find the...Ch. 3.4 - Refer to Exercise 14. Assume that l = 10.0 cm ...Ch. 3.4 - Prob. 27ECh. 3.4 - Refer to Exercise 16. Assume that T0 = 73.1 0.1F,...Ch. 3.4 - Prob. 29ECh. 3.4 - Prob. 30ECh. 3.4 - Prob. 31ECh. 3 - Prob. 1SECh. 3 - Prob. 2SECh. 3 - Prob. 3SECh. 3 - Prob. 4SECh. 3 - Prob. 5SECh. 3 - Let A and B represent two variants (alleles) of...Ch. 3 - The heating capacity of a calorimeter is known to...Ch. 3 - Sixteen independent measurements were made of the...Ch. 3 - If two gases have molar masses M1 and M2, Grahams...Ch. 3 - A piece of plywood is composed of five layers. The...Ch. 3 - The article Effect of Varying Solids Concentration...Ch. 3 - Prob. 13SECh. 3 - Prob. 14SECh. 3 - Prob. 15SECh. 3 - The mean yield from process A is estimated to be...Ch. 3 - The flow rate of water through a cylindrical pipe...Ch. 3 - Prob. 18SECh. 3 - The decomposition of nitrogen dioxide (NO2) into...Ch. 3 - Prob. 20SECh. 3 - A track has the shape of a square capped on two...Ch. 3 - Prob. 22SECh. 3 - Prob. 23SE
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