Example 6.22 From book: Concentrations of pollutants produced by chemical plants historically are known to exhibit behavior that resembles a lognormal distribution. This is important when one considers issues regarding compliance with government regulations. Suppose it is assumed that the concentration of a certain pollutant, in parts per million, has a lognormal distribution with parameters μ = 3.2 and σ = 1. What is the probability that the concentration exceeds 8 parts per million? Let the random variable X be pollutant concentration. Then = P(X8) 1- P(X ≤8). o : Since ln(X) has a normal distribution with mean μ = 3.2 and standard deviation σ = 1, [In(8) 3.21 P(X ≤ 8) = $ =(-1.12) = 0.1314. 1 = 1-P(X ≤8) 1-0.1314 = 0.8686 = 86.86% 8/10

Example 6.22 From book: Concentrations of pollutants produced by chemical plants historically are known to exhibit behavior that resembles a lognormal distribution. This is important when one considers issues regarding compliance with government regulations. Suppose it is assumed that the concentration of a certain pollutant, in parts per million, has a lognormal distribution with parameters μ = 3.2 and σ = 1. What is the probability that the concentration exceeds 8 parts per million? Let the random variable X be pollutant concentration. Then = P(X8) 1- P(X ≤8). o : Since ln(X) has a normal distribution with mean μ = 3.2 and standard deviation σ = 1, [In(8) 3.21 P(X ≤ 8) = $ =(-1.12) = 0.1314. 1 = 1-P(X ≤8) 1-0.1314 = 0.8686 = 86.86% 8/10

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 5SE: What does the y -intercept on the graph of a logistic equation correspond to for a population...

See similar textbooks

Similar questions

Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
Planetary Velocity The following table gives the mean velocity of planets in their orbits versus their mean distance from the sun. Note that 1AU astronomical unit is the mean distance from Earth to the sun, abut 93 million miles. Planet d=distance AU v=velocity km/sec Mercury 0.39 47.4 Venus 0.72 35.0 Earth 1.00 29.8 Mars 1.52 24.1 Jupiter 5.20 13.1 Saturn 9.58 9.7 Uranus 19.20 6.8 Neptune 30.05 5.4 Astronomers tell us that it is reasonable to model these data with a power function. a Use power regression to express velocity as a power function of distance from the sun. b Plot the data along with the regression equation. c An asteroid orbits at a mean distance of 3AU from the sun. According to the power model you found in part a, what is the mean orbital velocity of the asteroid?
Please can you solve this
The numbers of polio cases in the world are shown in the table for various years. Year Number of Polio Cases (thousands) 1988 1992 1996 2000 2005 2007 350 138 32 6 3.2 1.3 Let f(t) be the number of polio cases (in thousands) t years after 1980. Copy the data to Desmos to draw a scatterplot of the data. Make sure to adjust the years so they represent years after 1980. a) Is it better to model the data with a linear or with an exponential model? Select an answer b) Use regression in Desmos to find an appropriate model for f. Make sure to check Log mode in the parameter window in Desmos if you are fitting an exponential model. f(t) places. Round the coefficients to 4 decimal Hint: Use the variable t from the drop down menu when entering the equation. Do not just type in t. c) Predict the number of polio cases in 2019. d) Find the approximate half-life of the number of polio cases. Round the answer to one decimal place. years
The following equations were estimated using the data in BWGHT: log(bwght) = 4.66 - 0044 cigs + .0093 log(faminc) + .016 parity (.0059) (.22) (.0009) (.006) + .027 male + .055 white (.010) (.013) 1,388, R = .0472 and log(bwght) 4.65 – .0052 cigs + .0110 log(faminc) + .017 parity (.006) (.38) (.0010) (.0085) + .034 male + .045 white – .0030 motheduc + .0032 fatheduc (.011) (.015) (.0030) (.0026) n = 1,191, R2 = .0493. %3D
True or false: If a 90% CI for the population mean age is calculated to be [56 years, 66years] then this implies that approximately 90% of the population will be between 56 and 66 years old
The numbers of polio cases in the world are shown in the table for various years. Year Number of Polio Cases (thousands) 1988 1992 1996 2000 2005 2007 350 138 36 5 3.2 1.3 Let f(t) be the number of polio cases (in thousands) t years after 1980. Copy the data to Desmos to draw a scatterplot of the data. Make sure to adjust the years so they represent years after 1980. a) Is it better to model the data with a linear or with an exponential model? [Select an answer b) Use regression in Desmos to find an appropriate model for f. Make sure to check Log mode in the parameter window in Desmos if you are fitting an exponential model. f(t) Round the coefficients to 4 decimal places. Hint: Use the variable t from the drop down menu when entering the equation. Do not just type in t. c) Predict the number of polio cases in 2014. d) Find the approximate half-life of the number of polio cases. Round the answer to one decimal place. years
The numbers of polio cases in the world are shown in the table for various years. Year Number of Polio Cases (thousands) 1988 1992 1996 2000 2005 2007 350 138 33 3 3.2 1.3 Let f(t) be the number of polio cases (in thousands) t years after 1980. Copy the data to Desmos to draw a scatterplot of the data. Make sure to adjust the years so they represent years after 1980. a) Is it better to model the data with a linear or with an exponential model? [Select an answer b) Use regression in Desmos to find an appropriate model for f. Make sure to check Log mode in the parameter window in Desmos if you are fitting an exponential model. f(t) Round the coefficients to 4 decimal places. Hint: Use the variablet from the drop down menu when entering the equation. Do not just type in t. c) Predict the number of polio cases in 2013. d) Find the approximate half-life of the number of polio cases. Round the answer to one decimal place. years
The following are the cystatin C levels (mg/L) for the patients described in Exercise 15 (A-17).Cystatin C is a cationic basic protein that was investigated for its relationship to GFR levels. Inaddition, creatinine levels are also given. (Note: Some subjects were measured more than once.)Cystatin C (mg/L) Creatinine (mmol/L)1.78 4.69 0.35 0.142.16 3.78 0.30 0.111.82 2.24 0.20 0.091.86 4.93 0.17 0.121.75 2.71 0.15 0.071.83 1.76 0.13 0.122.49 2.62 0.14 0.111.69 2.61 0.12 0.071.85 3.65 0.24 0.101.76 2.36 0.16 0.131.25 3.25 0.17 0.091.50 2.01 0.11 0.122.06 2.51 0.12 0.062.34Source: Data provided courtesy of D. M. Z. Krieser, M.D.(a) For each variable, compute the mean, median, variance, standard deviation, and coefficient ofvariation.(b) For each variable, construct a stem-and-leaf display and a box-and-whisker plot.(c) Which set of measurements is more variable, cystatin C or creatinine? On what do you base youranswer?
The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in F) for that month. The past year's usage and temperatures are in the following table: Usage/ Month Temp. 1000 Month 21 185.79 July. 24 214.47 Aug. 32 288.03 Sept. 47 424.84 Oct. 50 454.58 Nov. 59 539.03 Dec. Jan. Feb. Mar. Apr. May June Temp. 68 74 62 50 41 30 Identify which are the independent and dependent variables. Usage/ 1000 621.55 675.06 562.03 452.93 369.95 273.98
1.2 number 12 review