A biologist doing an experiment has a bacteria populationcultured in a petri dish. After measuring, she finds that there are98.5 million bacteria infected with the zeta-virus and 26.4 millioninfection-free bacteria. Her theory predicts that 20% ofinfected bacteria will remain infected over the next hour, while theremaining of the infected manage to fight off the virus in that hour.Similarly, she predicts that 20% of the healthy bacteria willremain healthy over the hour while the remaining of the healthy willsuccumb to the affliction. Modeling this as a Markov chain,use her theory to predict the population of non-infectedbacteria after 1 hour(s). [Round to 3 significant figures.]O a) 25 millionOb) 84.1 millionO c) 40.8 milliond) 99.9 million

Infected Non- Infected 20% 80% Infected 80% 20% Non- Infected To find - The population…

Answered: A biologist doing an experiment has a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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According to scientists, the cockroach has had 300 million years to develop a resistance to destruction. In a study conducted by researchers, 5,000 roaches (the expected number in a roach-infested house) were released in the test kitchen. One week later, the kitchen was fumigated and 18,857 dead roaches were counted, a gain of 13,857 roaches for the 1-week period. Assume that none of the original roaches died during the 1-week period and that the standard deviation of x, the number of roaches produced per roach in a 1-week period, is 1.4. Use the number of roaches produced by the sample of 5,000 roaches to find a 90% confidence interval for the mean number of roaches produced per week for each roach in a typical roach-infested house. Find a 90% confidence interval for the mean number of roaches produced per week for each roach in a typical roach-infested house. (Round to three decimal places as needed.)
Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables < cereals < nuts < corpse). Geochemical surveys take soil samples to determine phosphorous content (in ppm, parts per million). A high phosphorous content may or may not indicate an ancient burial site, food storage site, or even a garbage dump. Independent random samples from two regions gave the following phosphorous measurements (in ppm). Assume the distribution of phosphorous is mound-shaped and symmetric for these two regions Region I: x1; n1 = 15 855 1550 1230 875 1080 2330 1850 1860 2340 1080 910 1130 1450 1260 1010 Region II: x2; n2 = 14 540 810 790 1230 1770 960 1650 860 890 640 1180 1160 1050 1020 (a) Use a calculator with mean and standard deviation keys to verify that x1, s1, x2, and s2. (Round your answers to one decimal place.) x1 = ppm s1 = ppm x2 = ppm s2 = ppm…
In 2022, the CDC reported that 12.5% of U.S. adults currently smoke cigarettes. From the same report, a random sample of 12,405 Ohioans was taken with 2543 being current smokers. Using α = 0.05, test whether the proportion of Ohioans that smoke cigarettes is different than the proportion of U.S. adults
The cuttlefish, a cephalopod and first cousin of the octopus, has the ability to camouflage to almost any natural sea environment instantaneously (within a few milliseconds). They are also able to camouflage to non-natural environments but not quite as quickly. A cognitive psychologist is interested in whether cuttles exhibit learning (by showing a reduction in reaction time) after repeated exposure to the same environment. Initially, 10 baby cuttlefish are individually placed in a tank with a checkerboard bottom and their reaction time (time to camouflage) is recorded. Over the next month the samecuttlefish are exposed to the same environment daily and at the end of the month each cuttlefish's reaction time is recorded again. The data are recorded in the table below. Reaction Time (seconds) Subject Before After 1 58 41 2 48 45 3 54 40 4 56 42 5 55 48 6 55 41 7 43 32 8 51 44 9 62 38 10 35…
Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables < cereals < nuts < corpse). Geochemical surveys take soil samples to determine phosphorous content (in ppm, parts per million). A high phosphorous content may or may not indicate an ancient burial site, food storage site, or even a garbage dump. Independent random samples from two regions gave the following phosphorous measurements (in ppm). Assume the distribution of phosphorous is mound-shaped and symmetric for these two regions. Region I: x,; n, = 15 875 1,080 2,330 1,850 1,860 853 1,551 1,230 2,340 1,080 910 1,130 1,450 1,260 1,010 Region II: x,; n, = 14 540 808 790 1,230 1,770 960 1,650 860 890 640 1,180 1,160 1,050 | 1,020 In USE SALT (a) Use a calculator with mean and standard deviation keys to verify that x,, S,, x2, and s,. (Round your answers to four decimal places.) X1 ppm S. = ppm X2 ppm 52 ppm (b) Let u, be the…
In a M/M/1 model, the average number of customers in the system is 16, and the average waiting time in the system (i.e., response time) is 53 minutes. Then, the average service time (in minutes) is 03.3125 03.11769 00.32075 00.30189
An experiment to test the effectiveness of regular treatments with fluoride varnish to reduce tooth decay involved 36 volunteers who had half of their teeth (the right side or left side, determined by a coin flip) painted with a fluoride varnish every six month for 5 years. At the end of the treatments, the number of new cavities during the treatment period was compared on treatment (fluoride varnish) side versus the control (no fluoride varnish) side. The appropriate statistical test for analyzing the results of this experiment is O Paired t test for a mean difference O One sample z test for a population mean O Two sample t test for a difference in means O One sample z test for a population proportion O Two sample z test for a difference in proportions
Carbon dioxide is known to have a critical effect on microbiological growth. Small amounts of CO2 stimulate growth of some organisms, whereas high concentrations inhibit the growth of most. The latter effect is used commercially when perishable food products are stored. A study is conducted to investigate the effect of CO2 on the growth rate of pseudomonas fragi, a food-spoiling organism. Carbon dioxide is administered at five predetermined different atmospheric pressures. The response measured was the percentage change in cell mass after 1-hour growing time. Ten cultures were used at each atmospheric pressure level, resulting in the following data: 0.0 .083 .29 .50 .86 62.6 50.9 45.5 29.5 24.9 59.6 44.3 41.1 22.8 17.2 64.5 47.5 29.8 19.2 7.8 59.3 49.5 38.3 20.6 10.5 58.6 48.5 40.2 29.2 17.8 64.6 50.4 38.5 24.1 22.1 50.9 35.2 30.2 22.6 22.6 56.2 49.9 27.0 32.7 16.8 52.3…
A pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, three samples of rats are selected with n=10n=10 in each sample. The first sample receives the drug every day. The second sample is given the drug once a week, and the third sample receives no drug at all (the control group). The dependent variables is the amount of food eaten by each rat over a 1-month period. These data are analyzed by an ANOVA, and the results are reported in the following summary table. Fill in all missing values in the table. (Hint: Start with the df column.) S.S. d.f. M.S. F Between 6.68 Within 4.35 TOTAL Use the =FDIST() function in Excel to locate the p-value for this ANOVA:p-value = Report p-value accurate to at least 6 decimal places.If you use a significance level of α=.05α=.05, what would you conclude about these treatments?
The aging Neotropical termites (Neocapritermes taracua) secrete a sticky, blue-colored liquid that they spew to intruding termites. The younger Neotropical termites secrete a liquid that lacks the blue component, so it is white in appearance. In an experiment that measured the toxicity of the blue substance, the researchers placed one drop of either the blue liquid or the white liquid on individuals of a second termite species, Labiotermes labralis. Of the 41 Labiotermes labralis that got the blue drop, 37 were immobilized. Of the 40 Labiotermes labralis that got the white drop, 9 were immobilized. Is the blue liquid toxic compared to the white liquid?
A group of 10-year-old boys were first ascertained in a camp for diabetic boys. They had their weight measured at baseline and again when they returned to camp 1 year later. Each time, a serum sample was obtained from which a determination of hemoglobin A1c (HgbA1c) was made. HgbA1c (also called glycosylated hemoglobin) is routinely used to monitor compliance with taking insulin injections. Usually, the poorer the compliance, the higher the HgbA1c level will be. The hypothesis is that the level HgbA1c is related to weight. The data in Table 11.28 were obtained. 11.95 Compute a rank correlation between change in weight and change in HgbA1c, each over 1 year. Use this measure to directly test the hypothesis that change in weight over 1 year is related to change in HgbA1c. Report a two-tailed p-value, and provide a 95% confidence interval for the underlying rank correlation.
A researcher selected a sample of 268 former student-athletes from a list of graduates of a large university. A total of 14% of the sample of athletes had earned graduate degrees as compared to 17% of all graduates. What is the Z obtained value?

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