(a) Experiment X is carried out nine times identically, and the value 5 is obtained all nine times. Calculate the mean by definition (4-12), then the standard deviation by definition (4-13). (b) Experiment Y is carried out nine times identically, and the integers 1 through 9 are each obtained once. Repeat the calculations of part (a) for this experiment. (c) For nine repetitions of experiment Z, the tally is that 1, 5, and 9 are each obtained three times. Repeat the calculations. (d) Explain any differences between the results in parts (b) and (c). Is standard deviation a reasonable measure of spread?
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Modern Physics
Additional Science Textbook Solutions
Tutorials in Introductory Physics
Lecture- Tutorials for Introductory Astronomy
College Physics: A Strategic Approach (4th Edition)
The Cosmic Perspective Fundamentals (2nd Edition)
Cosmic Perspective Fundamentals
Physics for Scientists and Engineers with Modern Physics
- In an experiment to understand the concepts of potential and kinetic energies, as shown below, suppose, you are making some errors while making the measurement. Initial Height H Final Height Ha If the weight used in the experiment is having an uncertainty of 0.9+ 0.01 N, the initial height is measured, with an uncertainty of 40 + 0.06 cm and the final height with an uncertainty of 26.9 + 0.06 cm. (Potential energies are calculated by the rmula weight x height) Calculate, 1) The absolute uncertainty in the calculated value of Initial Potential Energy (in Joules) = +0.00454 Joul 2) The absolute uncertainty in the calculated value of Final Potential Energy (in Joules) = +0.00323 Joul 3) The absolute uncertainty in the calculated value of Loss of Potential Energies (in Joules) = +0.0026 Joulearrow_forwardThe headway h is the average time between vehicles. On a highway carrying an average of 500 vehicles per hour, the probability P that the headway is at least t seconds is given by the following formula.t P = 0.87 (a) What is the limiting value of P? Explain what this means in practical terms. This means that the probability of finding very large headways is small (b) The headway can be calculated as the quotient of the spacing f in feet, which is the average distance between vehicles, and the average speed v, in feet per second, of traffic. Thus, the probability that spacing is at least f feet is the same as the probability that the headway is at least f/v seconds. Use function composition to find a formula for the probability Q that the spacing is at least f feet. Note: Your formula will involve both fand v. Q = (c) If the average speed is 90 feet per second, what is the probability that the spacing between two vehicles is at least 41 feet? (Round your answer to the nearest whole…arrow_forwardA total count of 1,000 was recorded in 100 minutes. Assuming the count rate (in per seconds) follows the poisson distribution. A) what is the probability of recording a zero count in a 10 second interval B) What is the uncertainty of your results in a?arrow_forward
- Which procedure(s) decrease(s) the random error of a measure ment: (1) taking the average of more measurements; (2) calibrating the instrument; (3) taking fewer measurements? Explain.arrow_forwardConsider the function: Z = where x = 13.36 ± 0.03 and, y = 6.27 ± 0.05 are two independent measured quantities, 1 PHY1509 PHYSICS SECTION each with its own error. Calculate the value of z and the standard error Az.arrow_forwardIn an experiment to understand the concepts of potential and kinetic energies, as shown below, suppose, you are making some errors while making the measurement. Initial Height H Final Height H. If the weight used in the experiment is having an uncertainty of 1.1+ 0.01 N, the initial height is measured, with an uncertainty of 45 + 0.09 cm and the final height with an uncertainty of 26.2 + 0.09 cm. (Potential energies are calculated by the formula weight x height) Calculate, 1) The absolute uncertainty in the calculated value of Initial Potential Energy (in Joules) = 2) The absolute uncertainty in the calculated value of Final Potential Energy (in Joules) = 3) The absolute uncertainty in the calculated value of Loss of Potential Enerqies (in Joules) =arrow_forward
- According to a mathematical model, the spring constant k, of a spring can be written as: k = 4² m T² where T is the period of oscillation of a mass m attached to a spring. You obtained the slope of a straight trendline from a plot of T² vs m, and estimated the uncertainty of this slope by drawing minimum and maximum slope lines (i.e. min-max method). Your result is slope = 9.841 [units] ± 0.0725 [units], where units represent the appropriate units. Assume your calculated value of k is 4.012 [units]. What will be the uncertainty in k? 0.296 [units] O 0.0725 [units] 0.00737 [units] O 0.0296 [units]arrow_forwardWater at 20°C flows past a half-body as shown in Fig. Measured pressures at points A and B are 160 kPaand 90 kPa, respectively, with uncertainties of 3 kPa each.Estimate the stream velocity and its uncertainty.arrow_forwardUncertainty in gamma Using Ruchardt's apparatus filled with air, y was determined to be 1.2 by measuring the period of motion which was found to be T = (0.81 ± 0.06) s. The equilibrium volume was estimated to be V = (4200 + 200) ml. Considering the uncertainties in only these variables find the corresponding uncertainty in y. Give your answer to 2 decimal places. Answer: xarrow_forward
- You repeat a measurement that contains random error many times, construct a histogram of your measurements and determine that the FWHM of the histogram is equal to 1.9. What is the uncertainty in one measurement, δn, equal to?arrow_forwardA publisher wants to estimate the mean length of time (in minutes) all adults spend reading newspapers. To determine this estimate, the publisher takes a random sample of 15 people and obtains the results below. From past studies, the publisher assumes σ is 1.5 minutes and that the population of times is normally distributed. 7 12 10 11 11 10 10 8 9 8 8 9 10 10 6 Construct the 90% and 99% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals. The 90% confidence interval is (enter your response here,enter your response here). (Round to one decimal place as needed.)arrow_forwardA series of four measurements of the ratio of the circumference to diameter of a disk are made. The results of these measurements are: 3.140, 3.133, 3.132, 3.133. The average of the four measurements is the experimental value for Pi-Lab and the accepted value is Pi = 3.141. What is the percent error of these measurements? a) 1 % b) 2% c) 0.5% d)0.2%arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON