The chemical benzene is highly toxic to humans. However, it is used in themanufacture of many medicine dyes, leather, and coverings. Governmentregulations dictate that for any production process involving benzene, thewater in the output of the process must not exceed 7,950 parts per million(ppm) of benzene. For a particular process of concern, the water samplewas collected by a manufacturer 25 times randomly and the sampleaverage x was 7960 ppm. It is known from historical data that the standarddeviation o is 100 ppm.(a) What is the probability that the sample average in this experiment wouldexceed the government limit if the population mean is equal to the limit?(b) Is an observed x = 7960 in this experiment a firm evidence that thepopulation mean for the process exceeds the government limit? Assumethat the distribution of benzene concentration is normal.

Given Information: Sample size n=25 Sample mean x¯=7960 Population standard deviation σ=100

Answered: The chemical benzene is highly toxic to…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A county environmental agency suspects that the fish in a particular polluted lake have elevated mercury levels. To confirm that suspicion, five striped basses in that lake were caught and their tissues were tested for mercury. For the purpose of comparison, four striped basses in an unpolluted lake were also caught and tested. The fish tissue mercury levels in mg/kg are given below. Sample I(From Polluted Lake) 0.523 0.723 0.523 0.623 0.523 Sample II(From Unpolluted Lake) 0.323 0.223 0.523 0.323 0.000 (a) Construct the 95% confidence interval for the difference in the population means based on these data. (b) Test, at the 5% level of significance, whether the data provide sufficient evidence to conclude that fish in the polluted lake have elevated levels of mercury in their tissue.
The National Institute of Standards and Technology (NIST) offers a wide variety of “standard reference materials” (SRMs) with accurately specified analyte concentrations. SRM 1951c is intended in part for “evaluating the accuracy of clinical procedures for the determination of total cholesterol . . . in human serum.” The certified total cholesterol is 6.244 ± 0.072 mmol/L. For the sake of this question, let’s treat 6.244 mmol/L as its “true” value (μ). We will use this standard to test a method with an intrinsic variability (for an experienced analyst) of σ = 0.131 mmol/L. **Please show written work! It is difficult to understand "text" work/answers with mathematical/statistical problems** 1. For what value of z does exactly 95% of the area under a Gaussian curve lie between ± z? Use this multiplier to find the range of measured cholesterol concentrations that would include 95% of the trials from the “parent population” (μ and σ) given above. 2. Calculate z for a trial in which the…
Joan's Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost-estimating purposes, managers use two hours of labor time for the plant- ing of a medium-sized tree. Actual times from a sample of 10 plantings during the past month follow (times in hours).2.1 2.2 1.7 1.6 2.3 3.1 1.5 2.6 2.4 2.2 With a .05 level of significance, test to see whether the mean tree-planting time differs from two hours. a. State the null and alternative hypotheses. b. Compute the sample mean. c. Compute the sample standard deviation. d. What is the p-value? e. What is your conclusion?
The regression equation for predicting the number of speeding tickets (Y) from information about driver age (X) is Y where b1=5.5 and bo= 0.16. How many tickets would you predict for a twenty-year-old O a. 8.7 O b. 110.16 Oc. Can't be determined O d. 2.3
The National Institute of Standards and Technology (NIST) offers a wide variety of “standard reference materials” (SRMs) with accurately specified analyte concentrations. SRM 1951c is intended in part for “evaluating the accuracy of clinical procedures for the determination of total cholesterol . . . in human serum.” The certified total cholesterol is 6.244 ± 0.072 mmol/L. For the sake of this question, let’s treat 6.244 mmol/L as its “true” value (μ). We will use this standard to test a method with an intrinsic variability (for an experienced analyst) of σ = 0.131 mmol/L. In three trials, you obtained the following cholesterol concentrations (all in mmol/L): 6.476, 6.590, 6.338. 1. Showing all work, calculate a 95% confidence interval for your measured cholesterol concentration and write it as an intermediate result (with guard digits). Does your measurement differ from μ at 95% confidence? 2. Repeat part 1 for 90% confidence and explain any change in your conclusion. 3. Another…
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 44 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that o = 8.00 ml/kg for the distribution of blood plasma.
The Specific Absorption Rate (SAR) for a cell phone measures the amount of radio frequency (RF) energy absorbed by the user's body when using the handset. Every cell phone emits RF energy. Different phone models have different SAR measures. To receive certification from the Federal Communications Commission (FCC) for sale in the United States, the SAR level for a cell phone must be no more than 1.5 watts per kilogram. A sample of 47 models was tested and the average of their Specific Absorption Rates (SARs) was found to be 1.18 watts per kilogram. Assume that the population standard deviation is 0.25 watts per kilogram. Construct a 90% confidence interval for the mean of the SARs for cell phones that received certification from FCC. Confidence interval:( , ) Interpretation: We are % confident that the mean of the SARs for cell phones that received certification from FCC is between watts per kilogram and watts per kilogram.
A study was carried out to determine the influence of a trace elementfound in soil on the yield of potato plants grown in that soil, defined asthe weight of potatoes produced at the end of the season. A large fieldwas divided up into 14 smaller sections for this experiment. For eachsection, the experimenter recorded the amount of the trace elementfound (in milligrams per metre squared) and the corresponding weightof the potatoes produced (in kilograms). This information is presentedin the worksheet ‘Dataset5’ in the Excel document. Define X as thetrace element amount and Y as the yield.1. Draw a scatterplot of your data set.Page 52. Calculate the coefficients of a linear equation to predict the yieldY as a function of X.3. Calculate the correlation coefficient for the paired data values.4. Set up the framework for an appropriate statistical test to establish if there is a correlation between the amount of the trace element and the yield. Explain how having the scatterplot referredto…
A screening test for a newly discovered disease is being evaluated. To determine the effectiveness of the new test, it was administered to 880 workers, and 120 of the individuals diagnosed with the disease tested positive. A negative test finding occurred in 50 people who had the disease. A total of 40 persons not diseased tested positive for it. Construct a 2 x 2 table similar to Table 12-1 and calculate the following: 1. Prevalence of the disease 2. Sensitivity 3. Specificity 4. Predictive value positive 5. Predictive value negative 6. Likelihood ratio positive 7. Likelihood ratio negative 8. Overall accuracy.
Refer to the following morbidity and mortality statistics for Community X for 2008. Total One-Year Population: 250,000 Population of Women 15-44: 75,000 Number of live births: 6,000 Total Deaths: 2,260 Number of infant deaths: 120 Deaths from heart disease: 222 Deaths from Cancer: 115 Deaths from Stroke: 90 Number of persons diagnosed with cancer 10,500 Calculate the following: Infant Mortality Rate _____________________________________ Prevalence of cancer for 2008 _____________________________ Crude Death Rate ______________________________________ Cause-specific mortality rate for stroke…
The owner of a new car conducts a series of six gas mileage tests and obtains the following results, expressed in miles per gallon: 3., 22.7, 21.4, 20.6, and 21.4. 20.9. Find the mode for these data.
Phosphorous is a chemical that is found in many household cleaning products. Unfortunately, phosphorous also finds its way into surface water, where it can harm fish, plants, and other wildlife. Two methods of phosphorous reduction are being studied. At a random sample of 7 locations, both methods were used and the total phosphorous reduction (mg/L) was recorded. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. Things that are labelled i underneath a b c, etc are all part of that part.

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