The drainage loading on a stormwater collection system is normally distributed with mean 1.2 million gallon per day (MGD) and standard deviation 0.4 MGD. Compute the system capacity, i.e., Design Life level (DDL), of the systems with a design life of 15 years and maximum risk of failure of 0.15 over its design life
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- a life time of a certain brand of tires is approximately normally distributed with a mean of 42,500 miles with a standard deviation of 3,200 miles. for how many miles should the warranty be if the company want 88% of the tires to outlast the warrranty?A particular manufacturing design requires a shaft with a diameter of 21.000 mm, but shafts with diameters between 20.990 mm and 21.010 mm are acceptable. The manufacturing process yields shafts with diameters normally distributed, with a mean of 21.005 mm and a standard deviation of 0.006 mm. Complete parts (a) through (d) below. a. For this process, what is the proportion of shafts with a diameter between 20.990mm and 21.000 mm? The proportion of shafts with diameter between 20.990 mm and 21.000 mm is . (Round to four decimal places as needed.) b. For this process, what is the probability that a shaft is acceptable? The probability that a shaft is acceptable is . (Round to four decimal places as needed.) c. For this process, what is the diameter that will be exceeded by only 2.5% of the shafts? The diameter that will be exceeded by only 2.5% of the shafts is 17.0118 mm. (Round to four decimal places as needed.) d. What would be your answers to parts (a) through…A study was conducted to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction. With a substrate concentration of 1.6 moles per liter, the reaction was run 16 times, with an average velocity of 7.7 micromoles per 30 minutes and a standard deviation of 1.6. With a substrate concentration of 1.9 moles per liter, 12 runs were made, yielding an average velocity of 8.9 micromoles per 30 minutes and a sample standard deviation of 1.2. Is there any reason to believe that this increase in substrate concentration cause an increase in the mean velocity of the reaction of more than 0.5 micromole per 30 minutes? Use alpha 0.01
- Following maintenance and calibration, an extrusion machine produces aluminum tubing with a mean outside diameter of 2.500 inches. As the machine functions over an extended number of work shifts the combination accumulated deposits and mechanical wear causes the mean diameter to drift away from the desired 2.500 inches. For a recent random sample of thirty-four tubes, the mean diameter was 2.491 inches and the standard deviation was 0.027 inches. Does the machine appear to be in need of maintenance and calibration (use α = 0.01)? Also, determine the p-value for the test. A. Provide the hypothesis B. Provide the test statistics formula C. Conduct the calculations and provide results D. Discuss the decision of whether or not to reject the hypothesis E. Discuss the business conclusionFollowing maintenance and calibration, an extrusion machine produces aluminum tubing with a mean outside diameter of 2.500 inches. As the machine functions over an extended number of work shifts the combination accumulated deposits and mechanical wear causes the mean diameter to drift away from the desired 2.500 inches. For a recent random sample of thirty-four tubes, the mean diameter was 2.491 inches and the standard deviation was 0.027 inches. Does the machine appear to be in need of maintenance and calibration (use α = 0.01)? Also, determine the p-value for the test. a. Provide the hypothesis (2 Points) b. Provide the test statistics formula(s) (3 Points) c. Conduct the calculations and provide results (6 Points) d. Discuss the decision of whether or not rejecting the hypothesis (2 Points) e. Discuss the business conclusion (2 Points)The Merck Manual states that, for healthy adults, the mean number of milliliters of oxygen per deciliter of blood is 19.0. A company that sells vitamins claims that its multivitamin complex will increase the oxygen capacity of the blood. A random sample of 28 adults took the vitamin for six months. After blood tests, it was found that the sample mean was 20.7 ml of oxygen per deciliter of blood with a standard deviation of 6.7ml. a. At the 0.05 level, test the claim that the average oxygen capacity has increased. b. How much power do you have to detect a 3ml difference (from the null) in the average amount of oxygen in the blood? c. What sample size would you need to have 90% power to detect this observed difference?