Organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organisms/m3 (the article "Counting at Low Concentrations: The Statistical Challenges of Verifying Ballast Water Discharge Standards"t considers using the Poisson process for this purpose). (a) What is the probability that one cubic meter of discharge contains at least 5 organisms? (Round your answer to three decimal places.) .971 (b) What is the probability that the number of organisms in 1.5 m3 of discharge exceeds its mean value by more than two standard deviations? (Round your answer to three decimal places.) (c) For what amount of discharge would the probability of containing at least 1 organism be 0.997? (Round your answer to two decimal places.) m3
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- A middle school teacher believes that a reading rewards program results in a higher number of pages read per year after the program is completed. The teacher chooses a simple random sample of students and records the number of pages read per year before starting the program and after the program is completed. The results of the study are below What are the population parameters? Pick Before 813.25 192250.25 182875.22 After 904.95 What is the level of significance? Ex: 0.12 Mean Variance Observations Hypothesized Mean Difference 100 100 Is the two-sample hypothesis test a paired or unpaired t-test? Pick 198 t Stat P[T< t) one-tail tCitical one-tail P[T<=t) two-tail t Critical two tal Confidence Level What is the null hypothesis Ho? Pick 0.068 1.653 What is the alternative hypothesis H.? Pick 1.972 95% Should Ho be rejected or does Ho fail to be rejected? Pick What conclusion can be drawn from the data? Pick v evidence exists to support the claim that the mean number of pages read per…The average income tax refund for the 2017 tax year was $1997. Assume the refund per person follows the normal probability distribution with a standard deviation of $943. Use this model to answer the following questions. Don’t use Excel formulas – use the tables. Show the standardization and other calculations. a) For a randomly selected return, what the is probability that the refund exceeds $2500 ? b) For a randomly selected return, what the is probability that the refund is between $2000 and $3000? c) What is the 3rd quartile of the refund amount? d) The 20th percentile?Coal is carried from a mine in west virginia to a power plant in new york in hopper cars on a long train. The automatic hopper car loader is set to put 77 tons of coal into each car. The actual weights of coal loaded into each care are normally distributed with mean u= 77 tons and standard deviation 0= 1.1 ton. A. What is the probability that one car chosen at random will have less than 76.5 tons of coal? ( Round your answer to four decimal places.) B. What is the probability that 29 cars chosen at random will have a mean load weight x of less than 76.5 tons of coal? ( Round your answer to four decimal places) C. Suppose the weight of coal in one car was less than 76.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment. Suppose the weight of coal in 29 cars selected at random had an average x of less than 76.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why?
- The types of raw materials used to construct stone tools found at an archaeological site are shown below. A random sample of 1486 stone tools were obtained from a current excavation site. Raw Material Regional Percent of Stone Tools Observed Number of Tools as Current excavation Site Basalt 61.3% 893 Obsidian 10.6% 165 Welded Tuff 11.4% 179 Pedernal chert 13.1% 198 Other 3.6% 51 (A) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)Suppose a sample of O-rings was obtained and the wall thickness (in inches) of each was recorded. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed. 0.163 0.182 0.194 0.211 0.224 0.225 0.233 0.243 0.251 0.259 0.271 0.273 0.295 0.307 0.317 0.340 Click here to view the table of critical values for normal probability plots. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. Using the correlation coefficient of the normal probability plot, is it reasonable to conclude that the population is normally distributed? Select the correct choice below and fill in the answer boxes within your choice. (Round to three decimal places as needed.) A. No. The correlation between the expected z-scores and the observed data, normal population. does not exceed the critical value, Therefore, it is not reasonable to conclude that the data come from…According to Reader's Digest, 44% of primary care doctors think their patients receive unnecessary medical care. Use the z-table. a. Suppose a sample of 260 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care. E(p)= (to 2 decimals) (to 4 decimals) b. What is the probability that the sample proportion will be within ±0.03 of the population proportion? Round your answer to four decimals. c. What is the probability that the sample proportion will be within ±0.05 of the population proportion? Round your answer to four decimals. d. What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why? The probabilities would - Select your answer -increasedecreaseItem 5 . This is because the increase in the sample size makes the standard error, ,
- r a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 510 and a standard deviation of 170 . The grading process of this year's exam has just begun. The average score of the 40 exams graded so far is 526 . What is the probability that a sample of 40 exams will have a mean score of 526 or more if the exam scores follow the same distribution as in the past? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.According to a sociologist's research on U.S. residents' habits regarding religious faith, 38% of U.S. residents attend a religious service (any denomination) at least once per month. Suppose 310 U.S. residents are sampled. (Give results accurate to at least 4 decimal places.) a. Of the 310 people sampled, 132 respond that they attend a religious service at least once per month. What is the sample statistic p? p= 0.4258 b. Under the assumption that the sociologist's claim that 38% of U.S. residents attend a religious service at least once per month is valid, what is the probability that the survey in part (a) would result in a p that is at least as high as the one found? c. Under the assumption that the sociologist's claim that 38% of U.S. residents attend a religious service at least once per month is valid, what is the probability that the survey in part (a) would result in a p that is between 37% and 40%?Tourism is extremely important to the economy of Florida. Hotel occupancy is an often-reported measure of visitor volume and visitor activity (Orlando Sentinel, May 19, 2018). Hotel occupancy data for February in two consecutive years are as follows. Current Year Previous Year Occupied Rooms 1,360 1,386 Total Rooms 1,700 1,800 a. Formulate the hypothesis test that can be used to determine whether there has been an increase in the proportion of rooms occupied over the one-year period. Let pi = population proportion of rooms occupied for current year Pa= population proportion of rooms occupied for previous year Ho : Pi - Pa H.: Pi - P2 Select your answer Select your answer b. What is the estimated proportion of hotel rooms occupied each year (to 2 decimals)? Current year Previous Year c. Conduct a hypothesis test. What is the p-value (to 4 decimals)? Use Table 1 from Appendix B. p-value - Using a 0.05 level of significance, what is your conclusion? We Select your answer- vthat there has…
- According to AAA, the price of a gallon of regular, unleaded gas across gas stations in Ohio is normally distributed with a mean of $2.39 and a standard deviation of $0.15. If you randomly pick a gas station, what is the probability the price is exactly $2.46 per gallon? A) 0.14 B) 0 C) 1 D) 0.68Suppose a sample of O-nings waS obtained and the wall thickness (in inches) of each was recorded. Use a normal probability plot to assess whether the sample data could have a a come from a population that is normally distnbuted. 0.190 0.194 0.199 0.205 E 0. 0.214 0.213 0.233 0.249 0.264 0.276 0.288 0.292 306 0.308 0.311 0.317 Click here to vew the table of cntical values for normal probability_plots] to Click here to view page 1 of the standard normal distribution table Click here to vew page 2 of the standard normal distribution table 2 b ◦ Using the correlation coeficient of the normal probability plot, is it reasonable to conclude that the population is normally distnibuted? Select the correct choice below and fll in the answer boxes within your choice. (Round to three decimal places as needed.) ○ A. Yes. The correlation between the expected z-scores and the observed data, Therefore, it is not reasonable to conclude that the data come from a noral population. exceeds the critical…In a certain presidential election, Alaska's 40 election districts averaged 1,958.8 votes per district for a candidate. The standard deviation was 572.5. (There are only 40 election districts in Alaska.) The distribution of the votes per district for one candidate was bell-shaped. Let X = number of votes for this candidate for an election district. O Part (a) ....... O Part (b) O Part (c) Find the probability that a randomly selected district had fewer than 1,700 votes for this candidate. (Round your answer to four decimal places.) 0.3 Sketch the graph. 0.0007 0.0007 0.0006 0.0006 0.0005 0.0005 0.0004 0.0004 0.0003 0.0003 0.0002 0.0002 0.0001 0.0001 X 4000 X 4000 1000 2000 3000 1000 2000 3000 0.0007 0.0007 0.0006 0.0006 0.0005 0.0005 0.0004 0.0004 0.0003 0.0003 0.0002 0.0002 0.0001 0.0001 X 4000 1000 2000 3000 4000 1000 2000 3000 Write the probability statement. P( 0.62 O Part (d) Find the probability that a randomly selected district had between 1,800 and 2,000 votes for this…