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

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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?
Mercury is a persistent and dispersive environmental contaminant found in many ecosystems around the world. When released as an industrial by-product, it often finds its way into aquatic systems where it can have deleterious effects on various avian and aquatic species. The accompanying data on blood mercury concentration (µg/g) for adult females near contaminated rivers in a state was read from a graph in an article. 0.20 0.23 0.26 0.30 0.35 0.41 0.54 0.57 1.43 1.70 1.84 2.20 2.24 3.08 3.26 (a) Determine the values of the sample mean and sample median. [Hint: Σxi = 18.61.] (Round your answers to four decimal places.) - x = ? ~ x = ? Explain why they are different. There is heavy positive skewness in the data. They aren't different since the data is symmetric. There are an odd number of data values. There is heavy negative skewness in the data. The sample mean and sample median are never equal. (b) Determine the value of the 10% trimmed mean. (Round your answer to…
Mercury is a persistent and dispersive environmental contaminant found in many ecosystems around the world. When released as an industrial by-product, it often finds its way into aquatic systems where it can have deleterious effects on various avian and aquatic species. The accompanying data on blood mercury concentration (µg/g) for adult females near contaminated rivers in a state was read from a graph in an article. 0.20 0.23 0.24 0.30 0.35 0.41 0.54 0.57 1.43 1.70 1.82 2.20 2.24 3.08 3.24 (a) Determine the values of the sample mean and sample median. Hint: xi = 18.55. (Round your answers to four decimal places.) x== Explain why they are different. The sample mean and sample median are never equal.They aren't different since the data is symmetric. There is heavy negative skewness in the data.There are an odd number of data values.There is heavy positive skewness in the data. (b) Determine the value of the 10% trimmed mean.…
7.24 Diamonds, Part I. Prices of diamonds are determined by what is known as the 4 Cs: cut, clarity, color, and carat weight. The prices of diamonds go up as the carat weight increases, but the increase is not smooth. For example, the difference between the size of a 0.99 carat diamond and a 1 carat diamond is undetectable to the naked human eye, but the price of a 1 carat diamond tends to be much higher than the price of a 0.99 diamond. In this question we use two random samples of diamonds, 0.99 carats and 1 carat, each sample of size 23, and compare the average prices of the diamonds. In order to be able to compare equivalent units, we first divide the price for each diamond by 100 times its weight in carats. That is, for a 0.99 carat diamond, we divide the price by 99. For a 1 carat diamond, we divide the price by 100. The distributions and some sample statistics are shown below.20 Conduct a hypothesis test to evaluate if there is a difference between the average standardized…
B. What is the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute? The best predicted temperature when a bug is chirping at 3000 chirps per minute is____°F. C. What is wrong with this predicted value? The first variable should have been the dependent variable. It is unrealistically high. The value 3000 is far outside of the range of observed values. It is only an approximation. An unrounded value would be considered accurate. Nothing is wrong with this value. It can be treated as an accurate prediction.
B. What is the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute? The best predicted temperature when a bug is chirping at 3000 chirps per minute is____°F. C. What is wrong with this predicted value? The first variable should have been the dependent variable. It is unrealistically high. The value 3000 is far outside of the range of observed values. It is only an approximation. An unrounded value would be considered accurate. Nothing is wrong with this value. It can be treated as an accurate prediction.
STAT 3128 Homeowrk Section 8.1 - 8.3. Question 1. An article reports the following values for soil heat flux of eight plots covered with coal dust. 34.8 33.7 34.8 35.3 33.3 28.5 18.3 24.6 The mean soil heat flux for plots covered only with grass is 25. Assuming that the heat flux distribution is normal, does the data suggest that the coal dust is effective in increasing the mean heat flux over that for grass? Test the appropriate hypotheses at the significance level 0.05 (a) State the appropriate null and alternative hypotheses. (b) State the distribution of the test statistic and calculate its value. (c) Calculate the p-value or find the critical value for this test. (d) State the conclusion: either reject the null hypothesis or fail to reject the null hypothesis.
A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below. Africa Asia = 63.3 yr. 1 X,=65.2 yr. 2 o, = 9.1 yr. = 7.3 yr. n1 = 120 = 150
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
38. Climate change 2016 Data collected from around the globe (including the sea ice data of Exercise 23) show that the earth is getting warmer. The generally accepted explanation relates climate change to an increase in atmospheric levels of carbon dioxide (CO.) because CO, is a greenhouse gas that traps the heat of the sun. A standard source of the mean annual CO, concentration in the atmosphere (parts per mil- lion) is measurements taken at the top of Mauna Loa in Hawaii (away from any local contaminants) and available at ftp://aftp.cmdl.noaa.gov/products/trends/ co2/co2_annmean_mlo.txt. Global temperature anomaly is the difference in mean global temperature relative to a base period of 1981 to 2010 in °C. It is available at www.ncdc.noaa. gov/cag/data-info/global. Here are a scatterplot and regression for the years from 1959 to 2016: 0.75 0.50 0.25 0.00 325 350 375 400 CO2 Response variable is: Temp R squared = 89.7% s = 0.0885 with 58- 2 56 degrees of freedom Variable Coefficient…