Math

StatisticsProbability and Statistics for Engineering and the SciencesNonpoint source loads are chemical masses that travel to the main stem of a river and its tributaries in flows that are distributed over relatively long stream reaches, in contrast to those that enter at well-defined and regulated points. The article “Assessing Uncertainty in Mass Balance Calculation of River Nonpoint Source Loads” ( J. of Envir. Engr ., 2008: 247–258) suggested that for a certain time period and location, X 5 nonpoint source load of total dissolved solids could be modeled with a lognormal distribution having mean value 10,281 kg/day/km and a coefficient of variation C V = .40 ( C V = σ X / μ X ) . a. What are the mean value and standard deviation of ln( X )? b. What is the probability that X is at most 15,000 kg/day/km? c. What is the probability that X exceeds its mean value, and why is this probability not .5? d. Is 17,000 the 95th percentile of the distribution?BuyFind*launch*

9th Edition

Jay L. Devore

Publisher: Cengage Learning

ISBN: 9781305251809

Chapter 4.5, Problem 79E

Textbook Problem

Nonpoint source loads are chemical masses that travel to the main stem of a river and its tributaries in flows that are distributed over relatively long stream reaches, in contrast to those that enter at well-defined and regulated points. The article **“Assessing Uncertainty in Mass Balance Calculation of River Nonpoint Source Loads” ( J. of Envir. Engr., 2008: 247–258)** suggested that for a certain time period and location,

**a.** What are the mean value and standard deviation of ln(*X*)?

**b.** What is the probability that *X* is at most 15,000 kg/day/km?

**c.** What is the probability that *X* exceeds its mean value, and why is this probability not .5?

**d.** Is 17,000 the 95th percentile of the distribution?

Probability and Statistics for Engineering and the Sciences

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Use Equation (4.13) to write a formula for the...Ch. 4.5 - Sales delay is the elapsed time between the...Ch. 4.5 - As in the case of the Weibull and Gamma...Ch. 4.5 - What condition on and is necessary for the...Ch. 4.5 - Suppose the proportion X of surface area in a...Ch. 4.5 - Let X have a standard beta density with parameters...Ch. 4.5 - Stress is applied to a 20-in. steel bar that is...Ch. 4.6 - The accompanying normal probability plot was...Ch. 4.6 - A sample of 15 female collegiate golfers was...Ch. 4.6 - The accompanying sample consisting of n = 20...Ch. 4.6 - The article A Probabilistic Model of Fracture in...Ch. 4.6 - Construct a normal probability plot for the...Ch. 4.6 - The article The Load-Life Relationship for M50...Ch. 4.6 - Construct a probability plot that will allow you...Ch. 4.6 - The accompanying observations are precipitation...Ch. 4.6 - Use a statistical software package to construct a...Ch. 4.6 - Let the ordered sample observations be denoted by...Ch. 4.6 - The following failure time observations (1000s of...Ch. 4 - Let X = the time it takes a read/write head to...Ch. 4 - A 12-in. bar that is clamped at both ends is to be...Ch. 4 - Let X denote the time to failure (in years) of a...Ch. 4 - The completion time X for a certain task has cdf...Ch. 4 - Let X represent the number of individuals who...Ch. 4 - The article Computer Assisted Net Weight...Ch. 4 - When circuit boards used in the manufacture of...Ch. 4 - Exercise 38 introduced two machines that produce...Ch. 4 - The reaction time (in seconds) to a certain...Ch. 4 - Let X denote the temperature at which a certain...Ch. 4 - An oocyte is a female germ cell involved in...Ch. 4 - The article The Prediction of Corrosion by...Ch. 4 - Let t = the amount of sales tax a retailer owes...Ch. 4 - The mode of a continuous distribution is the value...Ch. 4 - The article Error Distribution in Navigation (J....Ch. 4 - The article Statistical Behavior Modeling for...Ch. 4 - Suppose a particular state allows individuals...Ch. 4 - Let Ii be the input current to a transistor and I0...Ch. 4 - The article Response of SiCf/Si3N4 Composites...Ch. 4 - Let Z have a standard normal distribution and...Ch. 4 - a. 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